Topic 8 – Measurementgoosantateresa.weebly.com/uploads/1/0/1/1/10112908/...e) Distance from Melbourne to Brisbane Exercise 8.2 – Which unit would you use to measure or estimate

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TEP023 Foundation Mathematics

Topic 8 – Measurement

Introduction

Exercise 8.1 – Choose the most likely measurement from the list given.

Object Measurement

a) Width of your thumb 200 km

2 m

20 cm

20 mm

20 m

2000 km

200 m

b) Length of a ballpoint pen

c) Width of a netball court

d) Width of a car

e) Distance from Melbourne to Brisbane

Exercise 8.2 – Which unit would you use to measure or estimate the following?

a) The length of a netball court

b) The distance from Darwin to Alice Springs

c) The mass of a newborn human

d) The mass of an adult

e) The height of a 2 year old child

f) The distance from the sun to earth

g) The length of a thumbnail

Exercise 8.3 – How many kilograms are equivalent to:

a) 3 Gg b) 420 mcg

c) 5.0 mg d) 0.01 Mg

Exercise 8.4 – Write in symbols:

a) ten kilograms b) half a micrometre

c) two hundred kilolitres d) five million megagrams

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Study Guide Answers to Exercises

Conversion of Metric Units

Exercise 8.5 – Convert the following:

1. Length

a) 2750 mm = __________m b) 27 mm = __________m

c) 1.5 km = __________m d) 0.004 km = __________m

e) 0.006 km = __________cm f) 0.115 km = __________cm

g) 2100 m = __________km h) 320 m = __________km

i) 17900 cm = __________km j) 30 cm = __________km

k) 500 mm = __________km l) 7 km = __________mm

2. Mass

a) 29 g = __________kg b) 32 12 g = __________kg

c) 13.2 t = __________kg d) 0.09 t = __________kg

3. Time

a) 10 min = __________sec b) 1 12 min = __________sec

c) 34 min = __________sec d) 4 h = __________min

e) 13.25 h = __________min f) 0.4 h = __________min

g) 36000 s = __________min h) 36000 s = __________h

4. Volume

a) 1000 mL = __________L b) 550 mL = __________ L

c) 0.2 mL = __________L d) 13000 mL = __________kL

e) 0.002 L = __________mL f) 12 L = __________ mL

Exercise 8.6 – Find the following:

a) If a patient has five drinks of 150 mL each, how many litres of fluid has she had?

b) A bottle contains 500 salt tablets each containing 0.3 g of salt. How many grams of salt are contained in the bottle?

c) If a bandage measures 150 cm, and you require one which is 2.25 m long, how many centimetres short is the bandage you have?

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Rates

Exercise 8.7

1. Write each pair of quantities as a rate in its simplest form.

a) 6 km; 2h = km/h b) 20 kg; $5 = kg/$

c) $315; 7 days = $ /day d) 60 km; ½ h = km/h

2. A woman walks 12 km in 3 hours, her speed is __________km/h.

3. A boy swims 10 meters in 10 seconds, his speed is __________m/s.

4. An aircraft flies 600 km in 2 hours, its speed is __________km/h.

5. A jaguar can run 4 m in 0.2 seconds, its speed is __________m/s.

6. A helicopter flies 96 km in 30 minutes, its speed is __________km/h.

7. Oil costs $7.50 for 5 litres. What is the cost of the oil per litre?

8. A man is paid $240 for 30 hours work. What is he paid per hour? How many hours does it take to earn $1000?

9. A taxi charges $5.40 for a 6 km journey. What is the cost per km? How far could you travel for $10? (to the nearest km)

10. A girl swims 4 km per hour. How long does it take to swim 1 km?

11. Copy and complete these equivalent rates.

a) 1 km/min = km/h b) 40000 m/h = km/h

c) $50/kg = c/kg d) $50/kg= c/g

e) 90 beats/min= beats/sec f) 3t/h = kg/min

12. 15 kg of meat costs $118.50. What was the cost per kilogram?

13. I drove from Darwin to Katherine in 2.5 hours and covered 290 km. What was the average speed in km/h?

14. An Olympic sprinter can run 100 meters in 10 seconds.

a) What is her average speed in m/s?

b) What is this speed in km/h?

15. A medicine needs to be diluted at the rate of 20 mL of medicine per 1 L of water. How many millilitres of medicine would be needed to be mixed with 50 mL of water?

16. A ship’s pilot calculated the distance of the ship from a lighthouse as 5.6 n miles. How many kilometres is the ship from the lighthouse? (1 n mile = 1.852 km)

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17. Sound travels approximately 32 918 cm per second. If the sound of thunder is heard 12 seconds after the flash was seen, how far away was the lightening? Give your answer in:

(i) cm (ii) km to the nearest kilometer

18. A car trip of 573 km required 78 68 litres of fuel. What was the average

number of kilometres per litre?

Scientific Notation

Exercise 8.8 – Write in scientific notation.

a) 517 b) 932.5

c) 1 560 d) 12.75

e) 0.051 3 f) 0.000 008

g) 0.000 503 7 h) 357 000 000

Exercise 8.9 – Write in decimal notation (as a normal number).

a) 2.7 × 103 b) 4.06 × 104

c) 0.57 × 10-2 d) 1.95 × 10

e) 1 × 10-5 f) 2.9 × 10-3

g) 1.050 7 × 10-1 h) 2 × 104

i) 4.007 × 104


The hardness of a sample of water is expressed as 17 parts per million.

a) Express this in decimal notation.

b) Express this in scientific notation.

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Perimeter

Exercise 8.11 – Find the following perimeters:

a) b)

c) d)

e) f)


1. Find the unknown side of each triangle and hence the perimeter.

a) b)

c) d)

1.48 m

2.34 m

4.2 km

3.7 km

5 m

76 mm

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e)

2. The length of the diagonal of a square is 90 cm. Find the perimeter of the square.

Area

Exercise 8.13 – Find the following areas:

a) b)

c) d)

e) f)

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g) h)

i) j)

k) l)

m)

Exercise 8.14 – Convert the following:

a) 0.1 m2 to square millimetres b) 0.1 cm2 to square micrometres

c) 0.1 m2 to square micrometres d) 1000 mm2 to square metres

e) 15 cm2 to square metres

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1. Find the area of a rectangle with length 20 cm, and width 15 cm. Express your answer in square metres.

(Hint: you can either convert your linear dimensions to metres, or do the calculation in centimetres and convert the answer to square metres).

2. Find the area of a triangle with base 200 mm and height 100 mm. Express your answer in

(a) square centimetres

(b) square metres

3. Find the area of a circle with radius 5 cm. Express your answer in square metres.

4. Find the height of a trapezium with area 1.2 x 104 mm2 and side lengths

140 mm and 100 mm respectively given 1

2A a b h where a and b are

the length of the parallel sides and h is the height

5. A window is built in the shape of a rectangle surmounted by a semicircle. The dimensions of the rectangle are width 1.2 m and height 2.4 m. Find the quantity of glass required for the window.

6. A garden is made in the shape of a grassed rectangle (dimensions 10 m by 4 m) with a semicircular flower bed added to one end. A triangular paved area (dimensions 3 m, 4 m and 5 m) is in the middle of the grassed area.

(i) What is the total area of grass?

(ii) What is the total area of garden (grass and flower bed)?

(iii) The border of the garden is to be fenced. What length of fencing is

required?

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Volume

Exercise 8.16 – Find the volume of the following. All measurements are in centimetres. Give your answer to 1 decimal place where necessary.

a) b)

c) d)

e)

e) f)

Exercise 8.17 – Solve the following problems:

1. What is the area of a rectangular field with a length of 200 m and a width of 120 m?

2. A circular swimming pool has a diameter of 5.50 m and is filled to an average depth of 1.5 m. Calculate the volume of water in the pool.

a) in cubic metres

b) in litres

3. A cylindrical hot water tank has a diameter of 35 cm and is 150 cm high. How many litres will it hold?

4. A liquid container has the shape of a cube and measures 30 cm along the edge. How many litres will it hold?

5. The volume of a cylinder is 27.6 m3 and its height is 4 m. Find the area of its base.

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6. Petrol is stored in a cylindrical drum with a height of 120 cm, and a diameter of 90 cm. The petrol costs 53c/L. Find:

a) The volume of the drum.

b) The cost of filling the drum with petrol.

Application Questions


1. A regular six pointed star- shaped garden bed has sides 1 m long. How many 30 cm edging pieces are needed to edge the garden bed?

2. Amy is renovating her backyard. She has decided on an L – shaped garden bed and a triangle of grassy lawn as shown below:

a) The perimeter of the garden bed is to be bordered by edging wire that comes in 4m long rolls. How many rolls will Amy need to purchase?

b) The L shape is to have soil added to a depth of 20 cm. What volume of soil will be needed?

c) Amy decided to lay turf on the lawn area. At $16.95 per square meter, what will the lawn cost?

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3. The cube shown is to be covered in material. What is the surface area of the cube?

Surface Area is the total area of a shape found by adding up the area of each face of the shape.

4. A vase is 30 cm high and has a square base that measures 8.2 cm by 8.2 cm.

a) How much water could it hold when full in cm3?

b) Using 1 cm3 = 1mL, how many litres does it hold?

5. The diagram below represents a tent with a square base 3 m x 3 m. The seam between the canvas side walls is 3.25 m in length as shown. There are 4 triangular canvas walls in total. The floor of the tent is a heavy duty PVC. a) Determine the height of the triangular canvas wall of the tent.

b) Determine the total area of canvas required for the tent. Give your answer to the nearest whole number.

c) If the height of the tent is 2.46 m, calculate the volume of space inside the tent.

4 cm

3 m

3.25m

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Documents

Topic 8 – Measurementgoosantateresa.weebly.com/uploads/1/0/1/1/10112908/...e) Distance from Melbourne to Brisbane Exercise 8.2 – Which unit would you use to measure or estimate