Maths A - Chapter 8

8

syllabussyllabusrrefefererenceenceStrand:Applied geometry

Core topic:Linking two and three dimensions

In thisIn this chachapterpter8A Painting and wallpapering8B Tiling, carpeting and

kitchen planning8C Landscaping

Construction:The finishingtouches

MQ Maths A Yr 11 - 08 Page 289 Wednesday, July 4, 2001 5:44 PM

290

M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d

Finishing touches

With the shell of their home completed, Jaclyn and Kim now have to consider thefinishing touches.This chapter deals with:1. finishing the internal walls2. finishing the floors3. planning the kitchen4. landscaping.5. airconditioning

1

Draw nets for the following 3-D figures.

a b c

2

Calculate the outer surface area of the following figures.

a b

3

The sketch below shows a shed with a gable roof.

a

Draw a plan of the walls of the shed. Label your diagram with measurements.

b

Calculate the area of the walls.

c

Sketch the shape of the roof, labelling your diagram with dimensions.

d

Calculate the surface area of the roof.

e

Calculate the height of the roof above the walls.

f

Determine the pitch of the roof.

g

Draw a floor plan of the shed.

h

Sketch the northern elevation of the shed.

2.5 m

2.5 m1.8 m

2.4 m

6 m

10 m

N

EW

S

3 m

5 m


C h a p t e r 8 C o n s t r u c t i o n : T h e fi n i s h i n g t o u c h e s

291

4

The following diagram represents the floor plan of a kitchen. The bench/cupboardwidth around the perimeter is 590 mm.

a

Calculate the total floor area of the kitchen.

b

Determine the exposed floor area.

5

In landscaping his back yard, Jim removed soil to install a circular in-ground swim-ming pool with a 10-m radius and a depth of 1.5 m.

a

Calculate the volume of soil that Jim would need to remove.

b

If the soil that was removed to install the pool was used to top-dress the lawn, what

would be the depth of the top-dressing?

Finishing the walls

Two wall finishes commonly used today are paint and wallpaper.

Painting

When painting walls and ceilings, it is necessary to know the following information:1. area to be painted2. number of coats of paint to be applied3. coverage of the paint (number of square

metres covered by 1 litre of the paint)4. size and cost of the paint containers.

Jaclyn would like to paint all the ceilings of their Sturt home white. She prefers different pastel colours on the walls of each room. This is obviously more expensive than painting all the walls the same colour.

3300 mm

Bench

Ben

ch

1152

mm

Sink

Stov

e cu

pboa

rds

3590

mm

25 m

100 m

10 m


292


If we were to calculate the cost of paint for a room of a house, we would need tomake allowances for windows, doors and other openings. To calculate the areas ofthese, we would need measurements. Some plans indicate measurements of all featuresin great detail. In this case, it is a simple process to read dimensions from the plan, anduse these figures in calculations.

Since the floor plan of the Sturt design does not indicate detailed measurements, oreven a scale, it would first be necessary to determine the scale. (It is assumed that thediagram is drawn to scale.) Combining ruler measurements with the scale would thenproduce the actual dimensions of openings.

The ceiling of the whole Sturt design (including the verandah) is to be painted white. The paint covers 12 m2 per litre and can be purchased in 6-litre tins at $43.50 per tin. Two coats of paint are required. Use the floor plan of the Sturt design to calculate the cost of paint for the job.

THINK WRITE

Draw a diagram using the floor plan. Determine the dimensions of the ceiling in metres.

Calculate the area of the ceiling. Ceiling is 16 m × 8.925 mArea of ceiling = 16 m × 8.925 m

= 142.8 m2

Determine the quantity of paint required (remember, 2 coats).

No. of litres of paint required= 142.8 ÷ 12 × 2 litres= 11.9 × 2 litres= 23.8 litres

Find the number of tins required (round up if necessary).

No. of tins of paint = 23.8 ÷ 6= 3.97 tins

So 4 tins of paint are needed.Determine the cost of paint. Cost of paint = $43.50 × 4

= $174So the paint for the job would cost $174.

1 16 000 = 16 m

8925= 8.925 m

2

3

4

5

1WORKEDExample

From a printout of the floor plan of the Sturt design shown on the CD, determine:a the scale of the planb the width of the door and window in bedroom 3.

THINK WRITE

a Measure the length of one side of the house with a ruler, and compare this with the measurement indicated on the plan.

a 231 mm as measured with a ruler on the plan represents 16 000 mm on the house, that is 231 mm : 16 000 mm

Convert this to a scale. So the scale is 1 : 69

1

2

2WORKEDExample



293

Once the dimensions of the openings are known, the area to be painted can be calcu-lated by subtracting the area of the openings from the total area of the walls. It must berecognised that, if details are not supplied, and we are required to measure from a plan,these measurements are subject to slight errors. Answers obtained using this techniquewill be estimates.

THINK WRITE

b Measure door and window widths with a ruler.

b The door measures 12 mmThe window measures 26 mm

Use the scale to determine actual measurements.

The house measurements are 69 times the plan measurements∴ Door width = 12 mm × 69

= 828 mmWindow width = 26 mm × 69

= 1794 mm

1

2

The walls of bedroom 3, including the wardrobe doors, are to be painted light blue. The entry door and windows are both 2040 mm high, while the ceiling is 2400 mm high. A white undercoat (first coat) is applied, then a final coat of light blue. Both the blue and the white paint come in 2-litre tins at a cost of $21.50 per tin. Coverage of the paint is 14 m2/L. What would be the cost of the paint for bedroom 3?

Continued over page

THINK WRITE

Draw a plan of the walls opened out flat.

Calculate the total area of walls. Total area of walls = 12 m × 2.4 m= 28.8 m2

Determine the areas of the sections which are not to be painted (use scale and ruler measurements from the previous worked example).

Area of window = 1.794 m × 2.04 m= 3.66 m2

Area of door = 0.828 m × 2.04 m= 1.69 m2

Calculate the painted area. Area to be painted= total area walls − (area window + area door)= 28.8 − (3.66 + 1.69) m2

= 28.8 − 5.35 m2

= 23.45 m2

Find the quantity of paint required for each coat.

No. of litres of paint required per coat= 23.45 ÷ 14 L= 1.675 L

1

12 m3 m

2.4 m

3 m 3 m 3 m

2

3

4

5

3WORKEDExample


294 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d

WallpaperingAn alternative to painting the walls of a building is wallpapering. This is a job manypeople find they are capable of doing themselves. Standard wallpaper rolls are 10 mlong and 50 cm wide. The wallpaper is applied in drops (strips) from the top of thewall. If the paper displays a pattern, allowances must be made to match adjacent drops.When estimating the number of rolls of paper required for a job, it is normal practicenot to make allowance for windows or doors (unless, of course, these areas are large).It is also not possible to purchase part of a roll. Since the most common ceiling heightthese days is 2400 mm, this figure will be assumed unless otherwise stated.

THINK WRITE

Calculate the no. of tins required for each colour (round up if necessary).

No. of tins for each coat= 1.675 ÷ 2 tins= 0.8375 tins

So 1 tin is required for each coat.Determine the total cost of paint. Cost of 1 tin of white + 1 tin of blue

= $21.50 × 2= $43

6

7

How many rolls of wallpaper would be required to wallpaper the three walls of bedroom 1 in the Sturt design, if each roll is 50 cm wide and 10 m long? (Do not make allowance for any openings, and assume that the paper does not require pattern matching.)

THINK WRITE

Draw the plan of the walls out flat, showing dimensions.

Determine the total length of the walls to be papered.

Total length of walls to be papered= 4.1 m + 3.5 m + 4.1 m= 11.7 m

Calculate the number of drops of wallpaper required (remember to convert to the same units first).

No. of drops required = 11.7 m ÷ 50 cm= 11.7 m ÷ 0.5 m= 23.4

Round up the number of drops if it is not a whole number.

So 24 drops would be required

Calculate the total length of drops (each drop is 2.4 m long).

Each drop is 2.4 m long∴ Length of 24 drops = 24 × 2.4 m

= 57.6 mFind the number of rolls (each roll 10 m long).

No. of rolls = 57.6 m ÷ 10 m= 5.76

Round up the number of rolls if it is not a whole number.

∴ It would required 6 rolls of wallpaper to cover the 3 walls of bedroom 1.

1

4.1 m

2.4 m

3.5 m 4.1 m

2

3

4

5

6

7

4WORKEDExample


C h a p t e r 8 C o n s t r u c t i o n : T h e fi n i s h i n g t o u c h e s 295

WallpaperingThe aim of this investigation is to determine the effect of a pattern on applying wallpaper.

1 On a sheet of plain A4 paper, draw up a grid of 1-cm squares.

2 Cut this sheet into 2-cm-wide strips down its length.

3 Tape the ends of the strips, making sure that the pattern is continued correctly, to form one continuous length. Roll this length of paper to form your wallpaper roll.

4 Take another sheet of A4 paper. Its measurements are approximately 21 cm wide and 29.6 cm long. This piece of paper will represent the wall to be covered with your wallpaper.

5 With your sheet of paper in the portrait position (the direction you usually place paper for writing), cut strips from your roll of paper to wallpaper your wall, remembering to match the pattern of grids.

6 Did you need to waste wallpaper at the ends and beginnings of drops? What was the situation with your last drop? What would be the effect of large patterns in wallpapers?

7 Write up this investigation under the headings:a aim of investigationb procedurec resultsd conclusion/s and recommendation/s.

inve

stigationinvestigatio

n

remember1. When estimating the cost of paint required for a job, we need to know the area

to be painted, the number of coats required, the paint coverage, and the sizes and cost of the paint tins.

2. When detailed measurements are not indicated, estimates are obtained from the plan using the scale.

3. Remember to make allowances for openings when estimating painting areas.4. Wallpaper comes in rolls 10 m long and 50 cm wide. Determine the length of

wall to be papered, making no allowance for openings, unless they are large.5. For painting and wallpapering, assume a ceiling height of 2400 mm, unless

otherwise stated.

remember



Painting and wallpapering

1 A 10-m by 15-m recreation hall needs its ceiling painted with two coats of whitepaint. The paint covers 12 m2/L and can be bought in 4-litre tins at $36 per tin.Complete the following to calculate the cost of paint for the job.a Label the measurements of the ceiling on a diagram.b Area of ceiling =c No. of litres of paint required for two coats =d No. of tins of paint =e Cost of paint =

2 If the paint in question 1 was supplied in 3-litre tins for $27 per tin (the same priceper litre), what would be the cost of the paint?

3 The front elevation of a garage shows a roller door measuring 5 cm square on theplan. If the scale of the plan is 1:50, how many litres of paint would be required togive the roller door 3 coats, if the paint coverage is 14 m2/L?

4 A bedroom, 3.8 metres square, has built-in wardrobes from floor to ceiling completelydown one wall. The exterior wall has a window 1000 mm by 900 mm. Calculate thenumber of tins of paint required for two coats of the walls (excluding wardrobes andthe window) if the paint can be purchased only in 2-litre tins and the paint has acoverage of 12 m2/L. (Assume a ceiling height of 2400 mm.)

5 A church hall is 50 m by 20 m. Uniformly positioned on both sides down the lengthof the hall are 6 stained glass windows each measuring 0.5 m by 2 m. The ceiling is3 m high. The walls need to be coated with a varnish covering 10 m2/L. How muchvarnish would be required for two coats?

6 A rumpus room has the dimensions shown.a Determine the number of litres of each type of

paint required for the walls using a white undercoat which covers 12 m2/L and two coats of full gloss blue enamel paint with a coverage of 18 m2/L.

b How much paint would be required for the ceiling with a white undercoat(12 m2/L coverage) and two coats of white matt acrylic paint (16 m2/L coverage).

c The prices of the various types of paint are:undercoat $6.50 per litrefull gloss enamel $14.45 per litreacrylic $9.95 per litre.

Calculate the cost of painting the rumpus room if the paint can be purchased onlyin 2-litre tins.

7 Wallpaper can be purchased in rolls 50 cm wide and 10 m long. Ignoring openings inthe room, complete the following to determine the number of rolls of wallpaper requiredto cover the walls of a room that is 3.5 m square, and which has a ceiling 2.4 m high.a Label the net with wall widths and height.b Length of wall to be papered =c No. of drops of wallpaper =d Length of each drop =e Total length of all the drops =f No. of rolls required =

8AWORKEDExample

1

WORKEDExample

2

WORKEDExample

3

5 m8 m

2.4 m

Full wall of glass

WORKEDExample

4



297

8

If the walls of the rumpus room in question

6

were to be wallpapered instead ofpainted, how many rolls of wallpaper 50 cm wide and 10 m long would be required?

9

Sandra and Nick want to compare the cost of wallpapering their games room with thecost of painting. The costs are as follows.1. Wallpaper costs $22.50 for a roll which is 50 cm wide and 10 m long.2. Undercoat (1 coat) covers 12 m

2

/L and costs $6.50 per litre. (This is available in1-litre tins.)

3. Semi-gloss acrylic (2 coats required) covers 18 m

2

/L and costs $14 per litre (avail-able in 1-litre tins).

If their games room is 12 m long and 6 m wide, and has 2.4-m ceilings, advise thecost to wallpaper and to paint (ignore openings).

10

A standard wallpaper roll costs $22.50. Low sheen acrylic paint is available for$11.50 per litre. It covers 16 m

2

/L. Two coats are required. On a square-metre basis, isit cheaper to wallpaper or paint?

Finishing the floors

If a building is erected from a concrete slab on the ground, the slab (that is, the floor ofthe building) is frequently covered with tiles or carpet. In the upper levels of structures,where the floor is not a concrete slab, polished timber is sometimes selected.

Tiling

When tiles are laid on a floor, they are glued in place, then a

grout

mixture is rubbed between the tiles, similar to the way in which mortar is used to bind bricks together. View the Construction section of the CD which demonstrates tiling in action.

Many tiling patterns are quite intricate, sometimes depicting several geometric shapes. Often, tiles are cut and placed at various angles. To calculate the number of tiles required for a job is often complex. For this reason, any tiling problems in this text will quote a price which represents an average price per square metre of tiles laid with grout. Any calculated cost for a job will represent an estimate, because of wastage.

WorkS

HEET 8.1

GJGar

dner

MQ Maths A Yr 11 - 08 Page 297 Friday, July 6, 2001 9:03 AM


Sometimes, a tiling estimate is required from a floor plan which does not indicate detailedmeasurements. It is then necessary to use the plan scale first, to determine dimensions.

Estimate the cost of covering the floor below with tiles at a price of $42.50/m2 laid.

THINK WRITE

Calculate the area of the floor as a composite area of 2 rectangles.

Area of floor = area of 2 rectangles= (10 m × 8 m) + (4 m × 7 m)= 80 m2 + 28 m2

= 108 m2

Find the total cost, given the price per square metre.

Cost of tiling = $42.50 × 108= $4590

8 m

10 m

12 m

3 m

1

2

5WORKEDExample

A kitchen plan has an island bench in the centre. Give an estimate for tiling the floor at a cost of $45/m2 for laid tiles.

THINK WRITE

Use the plan scale to determine the dimensions.

Scale is 1 : 100So actual measurements are 100 times plan measurements.Length of room = 4 cm × 100

= 400 cm= 4 m

Similarly:Width of room = 2.5 mIsland bench is 2 m by 1 m

No tiling is required under the island bench. The area to be tiled is the area of the island bench subtracted from the area of the room.

Area of room = 4 m × 2.5 m= 10 m2

Area of island bench = 2 m × 1 m= 2 m2

So area to be tiled= area of room − area island bench= 10 m2 − 2 m2

= 8 m2

Calculate the cost of tiling. Cost of tiling = $45 × 8= $360

Island bench

Scale 1 : 100

1

2

3

6WORKEDExample



CarpetingAnother popular floor covering is carpet. This comes in rolls, and is purchased by the linear metre. (It is not necessary to buy the whole roll as it is with wallpaper.)

The carpet is generally laid in parallel strips. Because the width of a room is often not an exact multiple of the carpet width, there is wastage from the side of the last carpet strip laid (as with wallpapering). These offcuts are sometimes bound around the edges and used as scatter rugs.

If a carpet depicts a pattern which requires matching of strips, this also contributes to wastage. In our carpeting calculations, we will assume no pattern matching (unless otherwise stated), and that the carpet is laid in strips parallel to the longest wall.

Carpet can be purchased in rolls 3.66 metres wide at a cost of $75 per linear metre. What would be the cost of purchasing carpet for the floor shown in the diagram?

THINK WRITE

Draw the room, showing all dimensions.

Lay strips 3.66 m wide parallel to the longest side.

Lay the carpet in strips parallel to the 12-m side.

Determine whether strips all need to be the same length.

Two 12-m-long strips cover a width of 7.32 m (with some cut off at the edge of the 2nd strip).One 8-m-long strip covers to a width of 10.98 m (so some is cut off the side).

Find the total length of all strips. So the total length of the carpet= two 12-m lengths + one 8-m length= 32 m

Calculate the cost. Cost of carpet = $75 × 32= $2400

8 m

10 m

12 m

3 m

1

8 m

10 m

12 m

3 m

7 m

3.66 m

3.66 m

3.66 m

4 m

Strip 1

Strip 2

Strip 3

2

3

4

5

7WORKEDExample



CarpetingThe aim of this investigation is to determine whether the length of carpet required for a room depends on the direction of laying.

1 We’ll initially start with carpet that fits neatly when laid in either direction.

a Cut a piece of paper into strips that are 2 cm wide, tape the strips together, then roll them up to simulate a carpet roll.

b On a sheet of paper, draw the outline of a rectangle 8 cm by 6 cm. This represents the floor to be carpeted.

c Taking your paper roll, lay strips in the rectangle, parallel to the longer side (the 8-cm one), cutting the strips to the required length.

d How many strips did you need? What total length of the roll was required?

e Repeat your experiment, laying your strips of paper parallel to the 6-cm side. How many strips did you need? What total length of the roll was required?

f What do you conclude from the above?

2 Repeat the experiment with a rectangle 9 cm by 7 cm. What do you conclude?

3 Repeat again with a rectangle 7 cm by 6 cm. Note your conclusion.

4 Assume you work for a carpet firm, and your boss has asked you to investigate this matter. Write a report, detailing your findings.

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301

Kitchen planning

How you lay out your kitchen can have a great impact on how effectively you can workin it, and consequently, whether you enjoy or dread preparing meals in it.

Planning the kitchen

The floor plan of the Sturt design shows the kitchen as viewed from above. It indicates bench space with a sink and hotplates. Adjacent to the sink is a pantry, and space for a refrigerator is directly opposite. The plan does not show the types of floor cabinet and drawers beneath the bench, nor does it show any overhead wall cabinets.

The design and relative position of items in the kitchen are very important considerations, as a great deal of time is generally spent in food preparation. In order to make informed decisions in planning a kitchen, it is necessary to consider the following facts.1. The three major items used in the kitchen are the sink, hotplates/oven, and

refrigerator. These should be arranged in what is called the

work triangle

.2. Between these three items there should be sufficient bench space to allow for

food preparation and cleaning up afterwards.3. A set-down space of at least 450 mm should be provided beside the refrigerator

and hotplates/oven for safety as well as convenience.4. The oven and/or microwave can be built into a wall cabinet.5. It is best not to break up bench space by placing items in the middle of it.Your task is to place floor and wall cabinets in the kitchen of the Sturt design. Proceed as follows.

1

Choose from the range of kitchen cabinets (A to U) shown in 3-D format and top-view format on the following pages. Remember to consider the measurements carefully so cabinets fit in the available spaces.

2

Assume that the kitchen bench is 875 mm high.

3

On a sheet of graph paper, rule up a scale as indicated on the kitchen planner (shown on page 304).

4

Draw a floor plan of the kitchen on graph paper, marking the relative positions of the cabinets that you have chosen from the A to U list.

5

On graph paper, draw elevations of the three walls of the kitchen, showing all floor and wall cabinets.

This type of kitchen is known as a U-shaped kitchen. It is generally considered to be the most workable kitchen shape. Other kitchen shapes are:1. L-shaped kitchens

These are generally situated in a long, narrow room where the kitchen cupboards and major appliances lie along two adjacent walls.

1. Corridor kitchensAs the name implies, these kitchens are narrow rooms with cupboards placed on two opposite walls, leaving a passageway between them.

2. Galley kitchensThese are one-wall kitchens, usually found in dwellings where space is limited (home units, studios).

Investigate the G.J. Gardner CD and plans in newspapers or brochures to locate kitchens of the types described above.

G JGar

dner

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875

300400450

600800900

720

450

875

300400450

875

600800900

720

315 315720

590 315

875

600

595

720

595

600800900

360

875

600

875

600

875

1200

1980

590 315

2135

400

2135

800

875

895or

745

895or

745

1200

575

800

2135

700

820

495

1226

800

Kitchen Cabinets

720

(Source: Olympic Laminates Pty Ltd.)

A. Wall

B. Wall

C. Wall Corner

D. Range

K. Oven cabinet

J. 2 Drawers 600

I. 2 Drawers plus1 deep drawer 600

H. 4 Drawer 600

G. 4 Drawer 450(top quality metal runners standard)

L. Floor

M. Floor

N. Floor

T. Pantry cabinet 400

U. Pantry cabinet 800

P. Elevated rangecabinet 1200 (with black top front rail. Available in all models. Use 3 range doors 400)

O.Deep corner floor cabinet 900

Narrow corner floor cabinet 750

S. Deep pantry terminal shelf (available in limited styles)

R. Deep floor terminal shelf (available in limited styles)

Q. Wall terminal shelf

TERMINAL SHELVING

F. Microwave oven cabinet(wall mounted)

E. Preparation cabinet(bench and wall mounted)

PANTRY

WALL CABINETSNote: Glass doors are available for 400mm and 800mm wall units in limited styles. Wall cabinets measure 315mm front to back including door.

FLOOR CABINETSDeep floor cabinets measure 590mm from front to back, including the door. Narrow floor cabinets measure 440mm from front to back including the door.



800mm

Copy and use these models to plan your kitchen layout

WALL CABINETS FLOOR CABINETS

A. Single door wall cabinet G. 4 Drawer cabinets 450

A.WALL

CABINET300mm

315mm

A.WALL

CABINET300mm

315mm

A.WALL

CABINET400mm

315mm

A.WALL

CABINET400mm

315mm

A.WALL

CABINET450mm

315mm

A.WALL

CABINET450mm

315mm

A.WALL

CABINET450mm

315mm

G.DRAWERCABINET

450mm

G.DRAWERCABINET

450mm

M.FLOOR

CABINET

900mm

Two door floor cabinet 900

N. Three door floor cabinet 1200

N.FLOOR CABINET

1200mm

O.FLOOR CORNER

CABINET

745mmO. Floor corner cabinet

745m

m

895m

m

895mm

H. I. J. Drawer cabinets 600 4 Drawer 3 Drawer 2 Drawer

H.I.J.DRAWERCABINET

H.I.J.DRAWERCABINET

B.WALL CABINET

800mm

315mm

B. Two door wall cabinets

B.WALL CABINET

600mm

315mm

B.WALL CABINET

900mm

315mm

B.WALL CABINET

800mm

590mm

K. Oven cabinet

L. Single door floor cabinets 300

300mm

L. FLOOR CABINET

300mm400mm

L. FLOOR

CABINET

400mm

L. FLOOR

CABINET

Single door floorcabinets 400

590m

m1200mm

P. ELEVATED RANGE CABINET

745mm

895mm

745mm

895mm

O.FLOOR CORNER

CABINET

P. Elevated range cabinet 1200

TERMINAL SHELVESQ.

Terminal shelves-wall

315mm

315m

m

315mm 315mm

590m

m

590m

m

Q. WALL

TERMINALSHELF R.

WALLTERMINAL

SHELF

S. WALL

TERMINALSHELF

R. Terminal shelves

-deep floor

S. Terminal shelves

-deep pantry

PANTRYT. Pantry cabinet 400

400mm

T. PANTRY

CABINET

800mm

U. PANTRY

U. Pantry cabinet 800

800mm

M. FLOOR CABINET

M. FLOOR CABINET

Two door floor cabinet 800

600mm

M. FLOOR

CABINET

600mm

M. FLOOR

CABINET

600mm

M. FLOOR

CABINET

M. Two door floor cabinet 600

450mm

L. FLOOR

CABINET

450mm

L. FLOOR

CABINET

450mm

L. FLOOR

CABINET

Single door floorcabinets 450

C.WALL CORNER

CABINET

315mm

315mm 595m

m

C.WALL CORNER

CABINET

315mm

315mm 595m

m

D.RANGE CABINET

800mm

315mm

D.RANGE CABINET

600mm

315mm

D.RANGE CABINET

900mm

315mm

C. Wall corner cabinets

D. Range cabinets

E. Preparation cabinet

E.PREPARATION CABINET

800mm

315mm

E. Microwave oven cabinet

F.MICROWAVE

OVEN CABINET

700mm

495mm

Note: BREAKFAST BAR:Can be any number of floor units with 820mm deep bar top. (It is best to continue off a corner unit.) If you are using more than

1 individual unit in your plan copy extra shapes. All dimensions quoted are nominal and include the thickness of the door.

595mm 595mm440m

m

590mm

440mm

590mm

440mm

590mm

440mm

590mm

590mm

440mm

440mm

590mm

440mm

590mm

440mm

590mm

440mm

590mm

440mm

440mm

590mm

440mm

590mm

590mm

590m

m

590m

m

600mm600mm

590mm

440mm

440mm

590mm

440mm

590mm

440mm

590mm

440mm590mm

590mm440mm

440mm

590mm

440mm

590mm

Source: Olympic Laminates Pty Ltd.



Kitchen planner

100mm

500mm

1 m 2 m 3 m 4 m

1

2

4

3

5

6

6.5

Met

res



Tiling, carpeting and kitchen planning

1 Calculate the cost of laying tiles on the floor shown in this plan if tiles cost $45/m2.

2 The bathroom shown in the plan contains a shower and a vanity basin.a Determine the cost of tiling the floor at $42/m2.b Two walls of the shower are to be tiled to a

height of 1.8 m. What would this cost using tiles priced at $38/m2 laid?

3 A conference room measures 12 m by 6 m. Carpet is sold by the linear metre from rollsthat are 3.66 m wide. Draw diagrams for each of the following situations and determinethe length of carpet required to cover the floor if the carpet is laid:a parallel to the longer side.b parallel to the shorter side.

4 It was decided to put a border of 30-cm-square tiles around the perimeter of the confer-ence room in question 3 and to carpet the remainder of the floor in the centre.a Draw a diagram showing measurements and features on the floor.b Determine the number of tiles around the perimeter of the room.c Find the length of carpet required if it was laid parallel to the longer side.d How many linear metres of carpet would be needed if it was laid parallel to the

shorter side?

remember1. When tiling a floor, determine the area to be tiled, taking into account those

areas covered by other fixed objects.2. Tiling costs are quoted by the square metre.3. Carpet is manufactured in rolls and purchased by the linear metre.4. The carpet is laid in strips parallel to the longest side of a room. With non-

rectangular rooms, the carpet strips may be of different lengths. Draw a diagram to confirm lengths of all strips.

5. Kitchen cabinets and drawers are available in a variety of sizes. Floor cabinets are generally 875 mm high and 590 mm deep.

remember

8B

12 m

2 m8 m

15 m

WORKEDExample

5

WORKEDExample

6

SkillSH

EET 8.1

2000

3700

9002000900 500

WORKEDExample

7



5 A room is 14.2 m square. It can be tiled at a cost of $36/m2. In order to carpet the roomfor the same outlay, what priced carpet could be used? (Carpet can be bought by themetre from rolls that are 3.66 m wide.)

6 Refer to the kitchen cabinet plans on pages 302 and 303.

a Wall cabinets come in various sizes.

i What is the maximum height of the wall cabinets?

ii Give the size of a microwave oven cabinet.

iii A corner cabinet would take up how much space?

b Refer to the floor cabinets displayed.

i What are the dimensions of the oven cabinet?

ii Give the most common height of a floor cabinet.

iii What options are available for a corner floor cabinet?

iv What choice is there in the ‘non-corner’ pantry cabinet range?

c What floor area does the ‘Two-door floor cabinet 600’ occupy?

d What depth are the floor cabinets?

e How deep are the majority of the wall cabinets?

7 A kitchen measures 3.2 m by 3.6 m.

a Draw a scale floor plan of the kitchen.

b Two adjacent walls must be outfitted with a floor cabinet with drawers, an ovencabinet, a corner cabinet, a pantry cabinet and floor cabinets with shelving. Designa kitchen using the range of furniture on pages 302 and 303. Make sure that thedimensions of the furniture can be accommodated by the size of the kitchen. Pre-pare a scale drawing of your plan.

8 The two-door wall cabinet B (900 mm long) is available in pine timber. To seal the sur-face of the wood, it can be varnished. Ignore the thickness of the timber in thefollowing calculations and do not round figures.

a Calculate the total surface area of the doors, inside and outside.

b Determine the area of the 4 exterior surfaces of the cabinet. (Ignore the surfacewhich is attached to the wall.)

c Calculate the surface area of the shelf (top and bottom).

d Find the area of the 5 internal surfaces of the cabinet.

e What is the total area of the exposed surfaces of the cabinet?

f If the varnish covers 10 m2/L and the cabinet requires 2 coats, how much varnishwould the job require (to the nearest mL)?

9 The preparation cabinet houses electrical appliances (mixer, toaster, etc.) on the baseand smaller utensils on the three shelves above. If the tallest electrical appliance is40 cm, draw a plan of the cabinet showing the position of the three shelves. Justify theirplacement with an explanation.



307

The scale diagram below is a site plan for a block of land on which a house is to bebuilt.

1

Calculate the dimensions of the block of land.

2

How long is the perimeter of the block?

3

Concrete costs $130/m

3

. If the driveway is laid with concrete 5 cm thick, what wouldbe the cost of concrete for the job?

4

Calculate the dimensions of the house.

5

What is the floor area of the house in square metres?

6

If the house faces the same direction as the garage, in which direction does the

back

of the house face?

7

Carpet can be purchased in rolls 3.66 m wide. If the carpet strips are laid parallel tothe longer side of the house, how many metres of carpet would be required to coverthe floor of the house? (Ignore the internal walls of the house.)

8

If the carpet was laid parallel to the shorter side of the house, what length of carpetwould be required?

9

If the swimming pool is 1.5 m deep, what is its capacity in kL?

10

Give an estimate of the number of square metres of turf required to lay grass aroundthe pool inside the fenced area.

1

Scale 1 cm ⇔ 4 m

N

Garage

House

Driveway

Swimmingpool

Garden bed

Gar

den

bed

MQ 11A Qld - Chapter 08 Page 307 Monday, August 22, 2005 9:41 AM

308


Landscaping

With the house finishing touches almost completed, it is now time for Jaclyn and Kimto turn their attention to landscaping. Let’s begin by accessing this option on the CD.

In order to cost accessories that provide comfort in our daily lives, we must applysome of the mathematical techniques that were considered in the previous chapter.We’ll consider several landscaping applications by investigating some practical situ-ations. The selection includes:1. landscaping a garden bed2. building a gate and fence3. designing a sprinkler system4. airconditioning5. preparing a quote for a simple shed.

Landscaping

1

Choose the Sturt design from the CD and place it on the land. The size of the block available is 40 m by 40 m. The block size for this investigation is 30 m by 30 m. With the drawing option, construct a fence around the boundary. This will help with the relative placement of items on the land. It can be removed later, if necessary.

2

The house does not necessarily have to be positioned parallel to the road. Enter the option ‘Layout tips’ and decide the best direction for the house. Use the move/rotate/mirror options to achieve the optimum position.

3

This particular house design does not incorporate a garage. Position a carport/garage on the land where you would consider it to be most convenient.

4

Use the drawing tool to provide a driveway to the garage and a path to the front door.

5

Position the clothes hoist, and draw a path leading to it.

6

Draw any other options you would like to include (tennis court, swimming pool), then landscape with trees, remembering that they provide shade, but also drop leaves!

7

Use the measuring tool to determine the distance of the external walls of the house from the boundaries.

8

Measure the dimensions of the house with the measuring tool. Calculate the percentage of the land covered by the house.

9

Add any finishing touches, then print out your landscaped design.

G JGar

dner

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Landscaping a garden bedIn this activity we consider the construction of a 10-metre-square garden, raised above the ground, with treated pine as a border.

1 Draw a plan of the garden.Notes1. There are two options for the border:

(a) treated pine sleepers (200 mm wide, 75 mm deep) are sold in 2.4-metre lengths

(b) treated pine pole (100 mm wide, 75 mm deep) comes in 1.8-metre lengths.

2. The sleepers are twice as wide as the poles.3. Our garden bed is to be 400 mm high.

2 Draw two front elevations of the bed detailing the number of lengths of each type of pine required for the structure. (Remember, they come in different lengths).

3. Compare the cost of constructing the garden bed using sleepers with the cost of a pine pole structure. Which would you recommend?

4. Determine the cost of filling the garden bed with soil at $30/m3.

5. What would be the total cost of the project?

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n

Treated Pine Pole FROM• 75 x 100 x 1.8 m. $5.25 PLM. $525• 125 x 150 x 1.8 m. $10.15 PLM PLM

Treated Pine Sleepers• 200 x 75 mmx 2.4 m

$1850PLM

SkillSH

EET 8.3

SkillSH

EET 8.2



Building a gate and fence

Consider the gate shown in the illustration above. Construct a model as follows.

1 Cut 0.5-cm strips of paper to use for the pickets, the frame and the bracing.

2 Using 9 pickets as shown, assemble these evenly over a frame that consists of two vertical and three horizontal rails (adjust your frame, if necessary, to accommodate your pickets).

3 Provide a bracing strip between the two horizontal rails.

4 Assuming that the gate is 1 m wide, determine the scale of your model.

5 Measure the total length of your pickets. Using your scale factor, and the prices above, calculate the cost of the pickets required.

6 Similarly, determine the cost of the frame and bracing using treated pine fence rails.

7 What is the total cost of the gate?

Use a similar process to design a section of the fence illustrated above using treated pine fence palings and treated pine fence posts and rails. Decide on a height for the fence. Use the prices given to determine a cost per metre for the fence.

inve


n

Wet Rough Sawn Treated Pine FROM• 75 x 38 mm. $1.70 PLM• 75 x 50 mm. $2.20 PLM $170

PLM

Treated Pine Fence Palings • 150 mm x 1.8 m. $1.65 FROMTreated Pine Fence Plinth • 150 x 25 mm. $1.75 PLM Treated Pine Fence Post H4• 100 x 100 mm. $6.20 PLM Treated Pine Fence Rails • 75 x 38 mm. $1.70 PLM $165• 100 x 38 mm. $2.20 PLM • 75 x 50 mm. $2.20 plm • 100 x 50 mm. $2.95 PLM ea

Treated Pine Windsor Pickets FROM• 0.9 m. $1.35 • 1.2 m. $1.75• 1.5 m. $2.25 • 1.8 m. $2.75 $135

PLM



A sprinkler systemUnderground sprinkler systems are commonplace in suburban homes. In this investigation, we consider decisions that must be made to achieve a system which adequately fulfils the job of watering the required area.

For this activity we have access to sprinklers that can spray areas of the following shapes:

1. full circle

2. half circle

3. quarter circle

1 Let’s consider the placement of sprinklers in the rectangular lawn shown at right.a What problems do you notice?b What percentage of the lawn does it water?c What would be the length of underground

piping necessary for the system?d Would it make a difference to the length of

piping necessary if it was laid width-ways rather than length-ways?

2 You will have noticed areas of the lawn in the above diagram that do not receive water spray.a Investigate a placement for the sprinklers which would provide a 100%

coverage of the lawn. (Draw a scale diagram using a compass.)b What length of underground piping would be required in this case?

3 Some above-ground sprinklers provide circular patterns; others oscillate and spray in an approximately rectangular pattern. Investigate a design for an underground system using rectangular pattern sprinklers. Would it provide more efficient lawn coverage?

Two booklets available free in gardening stores provide a guide to watering. Produced by Pope, they are called Easy Guide to Installing Lawn Pop-up Systems and Easy Guide to When Should I Water. Sections of the former booklet are reproduced here. Study the printed material, then try to devise a system which would be appropriate for an area in your school grounds.

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20 m

30 m



The Pope Rating Points used in the example above are the recommended values for the ‘Professional 50 mm Spray Pop-Up’ shown in the illustration directly below. For areas where the water flow is low, the ‘Low Pressure Spray Pop-Up’ is recommended, with Pope Rating Points as indicated in the illustration at the bottom of the page.



Anyone contemplating the installation of an underground sprinkler system should take time to plan the position and types of Spray Pop-Ups carefully. A planning grid is provided on the following page.



Soil types and wateringOn the following page is an extract from a pamphlet produced by Pope entitled, Easy Guide to When Should I Water.

Study the information carefully, then answer the questions:1. How frequently should you water during hot weather if your soil is clay?2. Why should clay soil generally require watering less frequently than sandy

soil?3. Why is it beneficial to water in the evening?4. How would you adjust the watering recommendations if you lived in Tasmania?5. What is the benefit of aerating lawns in spring?6. If using a professional 50-mm spray pop-up on loam, what is the recommended

watering time?

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n



7. Overall, the professional 50-mm spray pop-up requires less watering than the other sprinkler systems. Which units are next on the list in terms of low watering times?

8. How high should couch grass be cut in winter?9. Why should the cool season grasses be cut higher?Find out the soil types where you live and at your school. Write a recommendation for care of the lawn and garden at each place.


316


Air-conditioning

It is quite common these days to air-condition part or all of a private dwelling. Air-conditioning single rooms requires a system which is usually built into the wall. For larger areas, units are built into the roof or an exterior wall. Some systems offer reverse cycle air-conditioning (these units provide cool air in summer and warm air in winter). Ducting to the rooms is usually provided between the ceiling and the roof.

1

Visit a store to obtain information on air-conditioning.

2

What types of units are available?

3

Investigate the ducting system required.

4

What costs are involved in purchasing various units?

5

What costs are incurred in installing the various types of unit?

6

What are the running costs in terms of electricity usage?

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n

Split Ducted Air ConditionerAdvantages:Above the ceiling or below the floor you won’t see it but you’ll feel the difference• Air can be delivered to an outlet in any room or area• The air flow rate to each outlet can be individually controlled• Zone control allows sleeping areas at night or living areas

during the day to be conditioned separately• Air outlets positioned throughout the conditioned space

provide positive air distribution with the elimination of ‘dead’ spots, air short cycling or draughts

• No noise indoors, ultra quiet outdoors• No need for large, unsightly fascia units• No need to put large holes in the walls or damage the building

structure• No costly maintenance is necessary, just regular cleaning of

the air filter by the owner• Hidden insulated ducting to each outlet minimises heat losses• Easy to use finger tip control of temperature and fan speed• Year round operation with cost efficient heating in Winter and

cooling in Summer• The split system design allows for optimum positioning of the

outdoor condensing unit

Features:A comprehensive range of models, with both cooling only and reverse cycle operation, is available from 7.0 kW to 18.0 kW output capacities• Pressed, heavy gauge, metal outdoor cabinet.

Enamel painted fro long life protection• Dynamically balanced aerofoil fan and motor

assemblies for low noise and vibration free operation

• 350 mm low profile indoor fan coil unit for easier installation

• Room thermostat with on/off, heat/cool and fan speed switching

• 3 speed, high static pressure, indoor fan to suit long duct runs

• Electrical, pressure and thermal safety controls• High efficiency lanced aluminium fin and copper

tube heat exchangers

MQ Maths A Yr 11 - 08 Page 316 Monday, September 24, 2001 7:16 AM


317

Preparing a quote for a simple shed

In this investigation we consider the quantities and types of material required for the construction of a simple shed. Once these have been determined, a quote for the supply of the goods can be prepared. This is an open-ended activity, allowing for flexibility of design and choice of construction materials. Prices quoted for materials represent an ‘average’ cost with respect to the range of quality.

The shed

1

Draw a rough sketch of a simple garden shed that would suit your needs.

2

Decide on measurements that would be suitable. These include:

a

size of slab (which is 100 mm thick)

b

dimensions of footings (consult the ‘Footings and slabs’ section in the previous chapter for suitable measurements)

c

height of walls (for a shed these need not be 2400 mm)

d

style and pitch of roof.

3

Prepare scale drawings of:

a

floor plan

b

all elevations.

4

Using cardboard, construct a simple model of your shed.

The slab and footings

5

Calculate the volume of concrete required for the footings and slab.

6

If concrete costs $130/m

3

, determine the cost for this part of the job.

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MQ Maths A Yr 11 - 08 Page 317 Thursday, July 5, 2001 11:00 AM


The walls7 The walls may be constructed from a

timber frame covered with a suitable cladding. Framing costs approximately $10/m2. Choose a cladding from one illustrated on the next page. Determine the length of weatherboard required, then calculate the cost.

Another alternative is colorbond sheet metal cladding. Colorbond costs approximately $12/m2.

A brick wall would cost approximately $55/m2 laid.

The roofConcrete tiles cost $35/m2.Colorbond metal sheets are $12/m2.

Preparing the quote8 Design a quote form detailing information such as:

a cost of footings and slabb cost of wallsc cost of roof.

9 Calculate the cost per square metre for your shed.

To keep the above calculations simple, we have ignored factors such as roof trusses, windows and doors. In reality, you could take your design to a building supplier who would use a computer program to determine the quantities of all materials that you would need. Frames and roof trusses could be assembled off site for you, other materials could be cut to size and the shed could be delivered to you in a ‘pre-fabricated’ state ready for you to assemble.

Hardies Newport Hardies SummitWeatherboard Weatherboard• 4200 x 170 mm $1565 • 4200 x 230 mm $2145



Landscaping

Questions 1–4 use information found in the investigation on landscaping a garden bed(see page 309). Bob is planning the construction of a retaining wall 7.2 m long and 1 mhigh. He can use treated pine sleepers or treated pine poles (which come in two sizes).

1 Imagine that you are planning a retaining wall constructed of treated pine sleepers.a What is the length of a sleeper?b How many sleepers would be required per row?c What is the width of a sleeper?d How many rows of sleepers would be required?e What number of sleepers would be needed for the wall?f What is the cost of one sleeper?g What would be the cost of the sleepers for the wall?

2 Now imagine that you are planning the retaining wall constructed of treated pine poles(75 mm × 100 mm × 1.8 m). Answer each part in question 1 above, for treated pinepoles of this size.

3 Repeat question 1 using treated pine poles 125 mm × 150 mm × 1.8 m as the buildingmaterial.

4 Write a paragraph comparing the merits of the three types of timber which could beused to construct the retaining wall.

Question 5 requires information that can be located in the investigation on building agate and fence (see page 310).

5 a The wet rough sawn treated pine is available in two sizes.i Explain what the following measurements represent.

75 × 38 mm75 × 50 mm

ii Which size is better value? iii If 5 boards of each type were stacked flat on top of each other in two piles, what

would be the difference in height of the two stacks?iv If you ordered the same length of the two boards and the difference in cost was

$5, what length of each type did you order?b Treated pine fence rails are available in 4 sizes:

i Which are the widest?ii Which are the thinnest?iii What are the smallest and largest cross-sectional areas?iv Of the two rails that cost the same per linear metre, which size is better value for

money?

remember1. Landscaping often requires planning, using scale drawings.2. Most frequently, landscaping requirements are an application of geometry

techniques and the mathematics of money.

remember

8C



6 Refer to the investigation on sprinklers (pages 311 to 314) for information relating tothis question.a According to the graph on page 312, if it took 25 seconds to fill a 9-litre bucket

from a tap turned on full, what would be the tap’s rating?b Give two combinations of professional 50-mm spray pop-ups that would be suitable

for the tap.c Give two combinations of low pressure spray pop-ups that would be suitable for

that rating.d If four quarter-sprinklers, each with a stream throw of 3 metres, were used to water

a lawn that is 6 metres square, draw a design showing the optimum position of thesprinklers. Calculate the percentage of the lawn receiving direct water from thespray.

7 This garden shed is 2.5 m wide, 1.5 m deep and 2 m high. It has colorbond walls anddoor, with a colorbond gable roof at a pitch angle of 20°. It is erected on a concrete slab100 mm thick with footings 200 mm wide and 200 mm deep around the perimeter.

a Calculate the volume of concrete in the footings.b Determine the volume of concrete required for the slab.c If concrete costs $130/m3, what is the cost of concrete for the job?d Calculate the area of colorbond in the walls and door.e Using the pitch angle of the roof, calculate the perpendicular height of the tri-

angular gable section. Hence determine the total area of these sections, front andrear.

f Use the pitch angle to determine the dimensions of the roof. Hence calculate theroof area.

g Determine the total area of colorbond.h Calculate the cost of the metal sheeting at $12/m2.i What is the total cost of materials for the shed?

SkillSH

EET 8.4

SkillSH

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WorkS

HEET 8.2



Wall finishing• The quantity of paint required for a job depends on the area to be painted, the paint

coverage and the number of coats. Allowance is made for openings.• Wallpaper is hung vertically in drops, and is purchased by the roll. In estimating the

number of rolls required, no allowance is made for openings.Floor finishing• The quantity of tiles necessary for a job depends on the area being tiled.• Carpet is laid in strips, generally parallel to the longest side of the room.Furnishing a kitchen• Kitchen cabinets and drawers come in a variety of sizes.• Careful planning using scale drawings leads to a kitchen design that is practical and

versatile.Landscaping• Landscaping provides pleasurable surroundings. Lawns, gardens, fences and sheds

contribute to the overall comfort of the occupants.

summary



1 A lounge room is 5.4 m by 4.2 m with a ceiling that is 2.4 m high. The window in the exterior wall measures 1.5 m by 1 m.

a Calculate the cost of painting the ceiling with 2 coats of white acrylic (coverage 16 m2/L) costing $11.50/L.

b The elevation of the plan shows the exterior windows of the lounge room having measurements of 6 cm and 4 cm. What is the scale of the plan?

c What would be the cost of painting the walls of the lounge with 2 coats of semi-gloss acrylic (coverage 18 m2/L) if the paint can be purchased in 1-litre tins at $14 per tin?

d Determine the cost of wallpapering the lounge at $21/roll. Wallpaper rolls are 50 cm wide and 10 m long (ignore openings).

2 An entertainment room with a view towards the mountains has dimensions as shown:a Calculate the area of the room.b What would be the cost to tile the whole floor at $38/m2

for laid tiles?c If the centre rectangular section was carpeted and the triangular

sections on the edges were tiled:i how much would the tiles for these sections cost?ii what would the carpet cost at $85/m2? (Carpet rolls are 3.66 m wide.) Indicate whether

there is a difference in cost depending on the direction in which the carpet is laid.

8A

CHAPTERreview

8B 5 m

5 m 5 m

11 m


C h a p t e r 8 C o n s t r u c t i o n : T h e fi n i s h i n g t o u c h e s 3233 Consider the design of a kitchen.

a What is meant by the ‘work triangle’?b What alternatives are available in wall cabinets to provide wall storage down the entire

length of a 3.4-m wall?c What volume does the wall corner cabinet occupy?d If the non-corner pantry cabinets are arranged with the shelves evenly spaced, what is the

distance between the shelves?

4 A plant nursery constructed a raised rectangular garden bed using treated pine sleepers to retain the soil. The bed, measuring 24 m by 12 m, was two sleepers high around the perimeter. (See page 309 for sleeper sizes and costs.)a How many sleepers would be required?b Calculate the cost of the sleepers.c If the bed was filled to within 20 cm of the top of the border, how much soil would be

required?d What would be the soil cost at $30/m3?

5 An animal enclosure was built using treated pine fence palings. The enclosure was 1.8 m high, surrounding an area 30 m by 15 m. (See page 310 for paling sizes and costs.)a How many palings would be required for the whole enclosure?b What would be the cost of the palings?c What area would it enclose?d If the enclosure had been 25 m by 18 m it would have provided the same area. Would the

same number of palings be required? How many?e An enclosure 20 m by 22.5 m also provides the same area. How many palings would be

required in this instance?f What can you deduce about the number of palings required and the shape of the

enclosure?

8B

8C

8C



6 Refer to the investigation on soil types and watering (pages 314 and 315) for information relating to this question.a Which type of soil (sand, loam or clay) provides the greatest drainage? Which provides

the least?b Other than for the sake of appearance, why should weeds be removed from a garden?c Why is it not advisable to spread too much fertiliser on lawns?d Explain the recommendation, ‘Thin/scarify your lawn in spring for healthy lawns and

efficient watering’.e Name a warm climate grass. Generally these grasses have a broader leaf than the cool

climate grasses. What advantage is this?f Clay soil requires watering less frequently but for a longer period of time than sandy soil.

Explain this.g Of the Original Series Sprinklers, the Capitol Sprinkler requires less watering time than

the other two. Why would you then choose one of the other two?h Why is it inadvisable to sprinkle for extended periods of time?

7 A garden tidy is constructed of durable metal in the shape of a rectangular prism with a lid. With dimensions 1510 mm by 750 mm and a height of 1000 mm, it offers protection against the weather for the storage of outdoor items. To protect against vermin, the structure stands on a concrete slab 100 mm thick.a Calculate the volume of concrete in the slab.b What would be the cost of the concrete at $130/m3?c Determine the area of metal required for the structure.d At $15/m2, what would be the cost of the metal?e If you were constructing this garden tidy in your back yard, what could you expect to pay

for materials?f What volume would the tidy store?g If the structure was used for storing wood, what would be the longest length that could be

stored in the tidy?

8C

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CHAPTERyyourselfourself

testyyourselfourself

8


Business

Maths A - Chapter 8