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Basic Measuring and Calculations
Formulas, Workings Hints and Tips
When working out mathematics
• Start by writing down the formula • Ensure you show all working out (Marks will
be awarded for working out) • Substitute the appropriate figures into the
formula • Apply the appropriate formulas to each part of
the equation
What are types of measuring tools?
• Four fold rule – ideal for measurements up to 1 metre in length
• Retractable metal tape - suitable for measurements from 1 metre to 10 metres
• Fibreglass tape - used for long measurements e.g. building setout
• Scale rule – used for scaling dimensions off plans
Unit Conversion
• When working out the quantity of materials all measurements must be in the same units e.g. metres NOTE : (As a general rule if a question is printed in millimetres it is often easier to convert it to metres at the beginning of the equation unless the question asks for it to be answered in metres)
• To convert units for e.g. 1.000 metres to millimetres x by 1000 = 1000 millimetres
• To convert from millimetres to metres e.g. 1000 millimetres ÷ 1000 = 1.000 metres
• For more information refer to page 151 of your text book table 5.1
What units of measurement are used in the building industry?
• Linear measurements – e.g. measuring a piece
of timber • Linear measurements – are in millimetres and
metres • Refer to page 151 of the text book for units of
measurement used in the building industry
How are materials measured (Lineal measurement) ?
• Linear measurements are measured in mm or metres e.g. measuring the length of a wall is measured in lineal metres
Brick wall
3.000 metres
• Therefore the lineal length of the brick wall is 3.000 metres long
How are materials measured (Lineal measurement) ?
• Linear measurements are measured in mm or metres e.g. measuring the length of each wall around a room and adding those measurements together
5.000 metres
2.00
0 m
etre
s
•The total length around the room = 5.0 + 2.0 + 5.0 + 2.0 = 14 lineal metres •Formula = P1 + P2 + P3 + P4 = Total lineal metres
How are materials measured (Lineal) ?
• Circumference of a circle is the metre length around a circular object e.g. The tape measure length around the rim of a water tank
Water tank
•Circumference of a circle = 2 x pi x r
•Circumference = 2 x 3.14 x 1.5
• Circumference = 9.42 metres
NOTE : The answer is measured in metres only because there is only one measurement in the equation
Radius 1.5 m
Area Formulas
How are materials measured (Area) ?
• Area is measured in mm ² or metres ² • Formula for area of a rectangle Area = Length
x Width (The answer is always followed by the ² symbol)
Swimming pool cover
6.0 metres
2.0
met
res
• Area = L x W
• Area = 6.0 x 2.0
• Area = 12.0 metres² Note : The answer is in metres² because there are two measurements in the equation
How are materials measured (Odd Shapes Area) ?
• Area is measured in mm ² or metres ² • Formula for area of a rectangle Area = Length
x Width
• Area A = L x W
• Area A = 5.0 x 2.0
• Area A = 10.0 metres² Area A
Area B
5.0 metres 2.
0 m
etre
s
2.0
met
res
3.0 metres
• Area B = L x W • Area B = 3.0 x 2.0 • Area B = 6.0 metres²
Total Area A + B = 10.0 + 6.0 =16 m²
How are materials measured (Area) ?
• Area is measured in mm ² or metres ² • Formula for area of a circle Area = Pie x R² • (The answer is always followed by the ² symbol for area)
• Area = Pie x R²
• Area = 3.14 x 2.0²
• Area = 12.57 metres² Note : The answer is in metres² because there are two measurements in the equation (Pie & Radius)
Diam
eter 4.0 m
Radius 2.0 m
Cover for circular swimming pool
How are materials measured (Area) ?
• Area is measured in mm ² or metres ² • Formula for area of a triangle Area = ½ x Base
x Height (The answer is always followed by the ² symbol)
• Area = ½ x Base x Height
• Area = ½ x 4.0 x 3.0
• Area = 6.0 metres² Note : The answer is in metres² because there are two measurements in the equation
4.0 metres
3.0
met
res
Cover for triangle shaped swimming pool
How are materials measured (Area) ? • Area is measured in mm ² or metres ² • Formula for area of an irregular shape • Area =( length A + length B) x Height • (The answer is always followed by the ² symbol for area)
• Area = (length A + length B) x Height
• Area = (3.0 + 2.0) x 1.5
• Area = 4.0 metres²
Note : The answer is in metres² because there are two measurements in the equation
3.0 metres
2.0 metres
1.5
met
res
2
2
2
Cover for irregular shaped swimming
pool
How are materials measured (Rectangle Volume) ?
• Volume is measured in mm ³ or metres ³ Formula for Volume = Length x Width x Depth
(The answer is always followed by the ³ symbol)
1.5
m
Volume = L x W x D Volume = 6.0 x 2.0 x 1.5 Volume = 18.0 metres³ Note : The answer is in metres³ because there are three measurements in the equation
Amount of water in the swimming pool
How are materials measured (Cylinder Volume) ?
• Volume is measured in mm ³ or metres ³ Formula for Volume = Pie x R² x Height (The
answer is always followed by the ³ symbol)
Volume = Pie x R² x Height Volume = 3.41 x 1.0 x 3.0 Volume = 9.42 metres³ Note : The answer is in metres³ because there are three measurements in the equation
3.0
met
res
1. 0 m radius
Amount of water in water tank
tank
How are materials measured (Triangular Prism Volume) ?
• Volume is measured in mm ³ or metres ³ • Volume = (½ x base x Height) x Length (The answer is always followed by the ³ symbol)
Volume = (½ x base x Height) x Length Volume = (½ x 3.0 x 2.0) x 5.0 Volume = 15.0 metres³ Note : The answer is in metres³ because there are three measurements in the equation
3.0 metres
2.0
met
res
Amount of oxygen inside the tent
How are materials measured (Odd Shapes Volume) ?
• Calculate the lineal length of concrete footings required & how much concrete is needed in metres³
Length = footing length – footing width
•Side 1 = 5.0 – 0.600 = 4.4m
•Side 2 = 2.0 – 0.600 = 1.4m
•Side 3 = 2.0 – 0 = 2.0m
•Side 4 = 2.0 – 0 = 2.0m
•Side 5 = 3.0 – 0.600 = 2.4m
•Side 6 = 4.0 – 0.600 = 3.4m= 15.6Lin/M
Volume = Lineal length x width x depth
5.0 metres 2.
0 m
etre
s
2.0
met
res
3.0 metres Volume = 15.6 x 0.600 x 0.400 = 3.74m³
0.600 m wide footing
4.0
met
res
NOTE : Footing depth 0.400 m x 0.600 wide
Stud quantity key points
When working out how many timber studs are in a timber frame wall:
• Divide the length of the wall by the stud spacing
• Round up the answer e.g. 7.2 say 8 • Then add 1 therefore 8 becomes 9 • Refer to page 164 of text book for an example
How are materials measured (Quantity or Number of Studs) ?
No. of studs (length of wall) + 1 (Extra stud) Stud spacing No. of studs (8.0metres) = 13.33 say 14 +1 = 15 studs 0.600 m
8.0 metres
Tim
ber s
tud
wal
l
Wall plates quantity key points When working out how many top and bottom
plates for a timber wall frame: • Divide the length of the wall by the length of
timber you are using • Multiply the answer by 2 because there is a top
plate & a bottom plate • Then round up the answer at the end of the
calculation • E.g. 7.4 lengths of timber becomes 8/6.0
How are materials measured (Quantity or Number of Plates) ?
No. of Top or Bottom plates = (length of wall) x 2 Available Timber length No. of Plates (8.0metres) = 1.48 lengths for 1 plate 5.4 m = 1.48 lengths x 2 for top & bottom plates = 2.96 round up to 3 = 3 lengths of 90 x 45 Radiata Pine @ 5.4 metres long
8.0 metres
Tim
ber s
tud
wal
l
Tim
ber s
tuds
Top
plat
e
Bot
tom
pla
te
How are materials measured (Quantity or Number of Bricks)
• Calculate the quantity of bricks required for the double brick building detailed below
(Allow 50 bricks per metre²)
12.0 metres
2.4
met
res
110 mm brickwork
110 mm brickwork
Area of brick wall = length x height
Area of brick wall = 12.0 x 2.4 = 28.8 m²
Area of 2 brick walls = 28.8 x 2 = 57.6 m²
No. bricks = wall area x No. of bricks/m²
No. of bricks required = 57.6 x 50 bricks
No. of bricks = 2880 Bricks
Plan view
Elevation
How are materials measured (Calculate The Cost Of Bricks)
• Calculate the cost of bricks required for the double brick building detailed below
(Bricks to cost $810 per 1000 bricks)
12.0 metres
2.4
met
res
110 mm brickwork
110 mm brickwork
Cost = (No. of bricks) x cost
Cost = (2880 bricks) x $810.00
Cost = 2.88 x $810.00
Cost = $2332.80
Plan view
Elevation Quantity
1000
Materials units • General timber comes in set lengths in increments of
300mm • Put 0.300 in your calculator & press ++ it should
increase by 0.3 of a metre every time you hit the equals button (This is a good way of remembering orderable lengths of timber available at the timber yard)
• Lengths range from 1800mm to 7200mm • Brickwork is measured by 1000 bricks or per pallet • Concrete is measured in cubic metres • Surface area measurements are in metres²
When ordering timber
• Start with the section size e.g. 90mm x 45mm • How the timber is finished e.g. (RS) rough sawn • Species of timber e.g. hardwood • Strength grading e.g. F8 • Number of pieces e.g. 5/6.0 • Order the longest lengths first & progress down to
the shortest • 90 x 45 RS hardwood F8 5/6.0 7/4.8 2/2.4 1/1.8
Rewrite the following Timber orders 2/6.1, 3/4.3, 9/5.0, 3/4.9, 5/2.3
90 x 45 F24 hardwood RS cost $ 3.50 per Lin/M • Answer = 90 x 45 RS Hardwood F24 2/6.3m,
12/5.1m, 3/4.5m, 5/2.4m •Lin metre length = no. x length
•Lineal metre length =2 x 6.3 = 12.6 metres
•Lin metre length =12 x 5.1 = 107.1 metres
•Lineal metre length =3 x 4.5 = 13.5 metres
•Lineal metre length = 5 x 2.4 = 12.5 metres
Total lineal metre length = 145.7 Lin/ Metres Cost = total Lin/M x Cost per Lin/Metres
Cost = 145.7 Lin/M x $3.50per Lin/M
Cost = $509.95
NOTE :Round up to the next increment of 0.3 of a metre e.g. 2.4 metres long
How are materials measured (Surface Area Rectangular Prism) ?
Surface Area is measured in mm² or Metres² SA= (area of base x 2) + (area of one side x 2) +
(area of one end x 2) SA =(4.0 x 2.0 x 2) + (4.0 x 3.0 x 2) + (3.0 x2.0 x 2) SA = (16) + (24) + (12) SA = 52 metres²
4.0 metres
3.0
met
res NOTE: Imagine you cut a box
down all corners & ended up with 6 sides then worked out the area of each side and added them together for a Total Area
How are materials measured (Surface Area Cone) ?
Surface Area is measured in mm² or Metres² Cone SA = (pie x R x length of incline) + ( pie x R²) Cone SA = (3.14 x 0.600 x 2.0) + (3.14 x 0.600²) Cone SA = (3.77) + (1.13) Cone SA = 4.9 metres² Note: Refer to page 159 of your text book for more information
0.600 Radius
2.0
met
res
How are materials measured (Surface Area Of A Cylinder) ?
Surface Area is measured in mm² or Metres² Cylinder SA= (Pie x R² x 2) + (2 x Pie x R x Height) Cylinder SA=(3.14 x 0.800² x 2) + (2 x 3.14 x 0.800 x 3.0) Cylinder SA= (4.02) + (15.08) Cylinder SA= 60.62 metres² Note: Refer to page 159 of your text book for more information 0.800m
Radius
3.0
met
res
How are materials measured (Surface Area Pyramid) ?
Surface Area is measured in mm² or Metres² Pyramid SA = (area of base) + (length of base ) x Inclined height x 4
Pyramid SA = (1.5 x 1.5) + (l.5 ) x 2.0 x 4 Pyramid SA =(2.25) +(0.75) x 8.0 Pyramid SA = 24 metres²
2.0
met
res
2
Note: Refer to page 159 of your text book for more
information
2
How are materials measured (Fractions & Percentages) ?
Percentages can be converted to fractions as follows: • 75 % can be entered into the calculator as 0.75 or 3 abc 4 function on the calculator • Therefore to convert a fraction to a percentage you
can divide 3 ÷ 4 = 0.75 or 75% or on the calculator 3 abc 4 then the equals button then the abc button will give you the same answer 0.75 or 75 %