MODULE 8 WORKBOOKPerimeter, Area and Volume

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7 May 2019

Contents

Lesson 1 p 3

Lesson 2 p 12

Lesson 3 p 24

Apply (Non-calculator) p 33

Apply (Calculator) p 37

2

Module 8

Perimeter, area and volume PODS Before continuing, make sure you have watched and have access to the following Pods.To find these, simply log in to GCSEPod and enter the codes given into the search bar (or click on the titles below).

1. Triangles | MATHS-33-001

2. Quadrilaterals | MATHS-33-002

3. Circles | MATHS-33-004

4. Composite Shapes | MATHS-33-003

5. Prisms | MATHS-33-006

Lesson 1

Basic area and perimeter

PODS

1. Triangles | MATHS-33-001

2. Quadrilaterals | MATHS-33-002

3. Circles | MATHS-33-004

3

Quiz

Watch the pod and answer the following questions.

1. Which of the following can be a unit of area?

a) cm

b) m

c) m2

d) cm3

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2. What is the area of a rectangle measuring 7cm by 4 cm?

a) 28cm

b) 28cm2

c) 11cm2

d) 22cm

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3. What is the perimeter of a rectangle measuring 8cm by 13cm?

a) 42m

b) 104cm2

c) 104cm

d) 42cm

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4. What is the area of this shape?

a) 84cm2

b) 44cm2

c) 42cm2

d) 19cm2

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4

5. Find the area of the shape below, rounding your answer to 2 decimal places.

a) 201.06cm2

b) 50.265cm2

c) 50.27cm2

d) 64cm2

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6. Find the circumference of this circle, rounding your answer to 1 d.p.

a) 113.1cm

b) 28.3cm

c) 9.4cm

d) 18.8cm

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7. Find the circumference of a circle with radius 4 cm, rounding your answer to 1 d.p.

a) 25.1cm

b) 201.1cm

c) 12.6cm

d) 50.3cm

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5

8. The area of a triangle is 54 cm2. The height of the triangle is 9cm. What is the length ofthe base?

a) 6cm

b) 12cm

c) 3cm

d) 18cm

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9. What is the area of this shape?

a) 45cm2

b) 36cm2

c) 22.5cm2

d) 90cm2

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10. What is the area of this shape?

a) 13cm2

b) 20cm2

c) 36cm2

d) 22cm2

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6

Practise

Practise basic area and perimeter.

Do not use a calculator.

1.

a) Write an expression for the perimeter of this shape, simplifying as necessary.

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b) If the perimeter is 34cm, find y.

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2. If the area of this rectangle is 160cm2, find the width.

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3. Find the area of this circle, leaving your answer in terms of 𝜋.

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4. The area of this trapezium is 24cm2. What is the height?

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5. Here is a triangle and a square. The area of the two shapes is identical.

Find the length of the side of the square.

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9

Practise

Practise basic area and perimeter.

You may use a calculator.

1. The diameter of a bicycle wheel measures 45cm. If the wheel turns 24 times, how farwould the bicycle go in metres? Give your answer correct to 2 d.p.

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2. Find the perimeter of this shape, rounding your answer to 2 d.p.

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3. Tom has a rectangular garden measuring 41m by 37m. He wants to put weed killerdown all over the lawn. The box says that it covers 60m2 of the lawn. How manyboxes should he buy?

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10

4. The area of a parallelogram is 54.7cm2. The base of the parallelogram is 9.1cm. Findthe perpendicular height of the parallelogram. Give your answer correct to 2 d.p.

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5. John has a circular plate that measures 7.1cm across. He wants to paint a rim on theplate. What is the circumference of the plate? Give your answer in cm correct to 1 d.p.

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11

Lesson 2

Compound area and perimeter

PODS

4. Composite Shapes | MATHS-33-003

Quiz

Watch the pod and answer the following questions.

1. Find the value of x.

a) 7m

b) 13m

c) 9m

d) 11m

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2. Find the value of y.

a) 7m

b) 5m

c) 3m

d) 1m

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3. What is the perimeter of this shape?

a) 60m

b) 65m

c) 72m

d) 74m

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4. What is the value of x?

a) 14m

b) 13m

c) 12m

d) 11m

………………………………………………………………………………………………………………………………………………………………..

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5. What is the value of y?

a) 9m

b) 6m

c) 7m

d) 4m

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14

6. What is the perimeter of this shape?

a) 94m

b) 92m

c) 108m

d) 85m

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7. Find the perimeter of this shape.

a) 24cm

b) 30cm

c) 48cm

d) 46cm

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15

8. Find the area of this shape, correct to 1 d.p.

a) 31.4cm2

b) 15.7cm2

c) 157.1cm2

d) 39.3cm2

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9. This shape is made up of 5 identical rectangles. What is the length of one of thoserectangles?

a) 6cm

b) 9cm

c) 7cm

d) 8.5cm

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16

10. What two shapes is this compound shape made from?

a) Rectangle and a trapezium

b) Rectangle and a parallelogram

c) Parallelogram and a trapezium

d) Rectangle and a triangle

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17

Practise

Practise basic area and perimeter.

Do not use a calculator.

1. Find the area of this shape.

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2. Find the shaded area.

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3. Find the area of this compound shape.

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4. Find the area of this shape.

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19

5. This shape is made up of five identical rectangles. Find the total area.

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20

Practise

Practise basic area and perimeter.

You may use a calculator.

1. Find the area of the shape below:

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2. Find the area of this shape. It has one line of symmetry and all lengths are given in cm.

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3. Find the shaded area. All lengths are given in metres.

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4. Find the perimeter of this shape, giving your answer correct to 1 d.p. All lengths are incm.

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5. Find the area of this shape, giving your answer correct to 2 d.p. All lengths are in cm.

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23

Lesson 3

Volume and Surface Area

POD

5. Prisms | MATHS-33-006

Quiz

Watch the pod and answer the following questions.

1. Which of the following can be a unit of surface area?

a) m2

b) cm

c) cm3

d) kg

………………………………………………………………………………………………………………………………………………………………..

2. Which of these shapes is NOT a prism?

a) Cube

b) Cuboid

c) Pyramid

d) Cylinder

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24

3. Find the volume of this prism.

a) 150cm

b) 150cm2

c) 150cm3

d) 190cm2

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4. How many faces does this prism have?

a) 3

b) 4

c) 5

d) 6

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5. What is the name of this prism?

a) Triangular pyramid

b) Triangular prism

c) Tetrahedron

d) Cuboid

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6. This pentagonal prism has cross-section with an area of an area of 21.5cm2 and alength of 45cm. What is the volume of the prism?

a) 967.5cm3

b) 66.5cm3

c) 322.5cm3

d) Not enough information

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26

7. Find the volume of a cube with sides 7cm.

a) 21cm3

b) 49cm3

c) 294cm3

d) 343cm3

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8. Find the surface area of a cube with sides 3cm.

a) 54cm2

b) 27cm2

c) 216cm2

d) 9cm2

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9. What is the volume of this cuboid?

a) 180cm3

b) 120cm3

c) 148cm3

d) 15cm3

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27

10. What is the surface area of this cuboid?

a) 105cm3

b) 142cm2

c) 210cm2

d) 156cm2

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28

Practise

Practise volume and surface area.

Do not use a calculator.

1. Find the volume of this prism.

………………………………………………………………………………………………………………………………………………………………..

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2. Find the surface area of this prism.

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29

3. Find the surface area of a cuboid measuring 4cm by 2cm by 9cm.

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4. Find the volume of this prism, leaving your answer in terms of 𝜋.

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5. Find the volume of this trapezoidal prism.

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30

Practise

Practise basic area and perimeter.

You may use a calculator.

1. Find the surface area of this prism.

………………………………………………………………………………………………………………………………………………………………..

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2. Find the surface area of this closed cylinder, giving your answer to 2 d.p.

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3. Find the surface area of this prism.

………………………………………………………………………………………………………………………………………………………………..

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4. Find the volume of this prism.

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5. The volume of a cuboid is 168cm3. The base of the cuboid measures 4cm by 6cm.What is the height?

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32

Apply

Apply what you have revised about perimeter, area and volume.

Do not use a calculator.

Remember

It is important that you remember the formulae for calculating the area of different shapes:

Rectangle and parallelogram = base x perpendicular height

Triangle = (base x perpendicular height) ÷ 2 – it is a very common error to forget to half this!

Circles: area = πr2 and circumference = πd – don’t muddle up the radius and diameter – the

diameter is the long one as it is the longer word!

Trapezium = 1/2 (top + bottom) × height

Don’t forget your units and whether they are squared (area) or cubed (volume)

For composite shapes, split them up on the drawing and check your lengths very carefully.

For surface area write out the area of each face first before adding them all together – check you have all of the sides.

1. The diagram shows the plan of a rectangular garden with two circular flower beds.Apart from the flower beds, the rest of the garden is covered in grass. Estimate thearea of the grass.

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2. Find 75% of the area of this triangle.

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3. Find the area of a circular plate where the diameter measures 18cm. Leave your

answer in terms of𝜋.

Area = 𝜋𝑟$

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4. Find the volume of this prism. You must state your units.

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34

5. A wall of a building has the shape below:

Joanna wants to paint the wall. The paint costs £4.70 for enough to cover 4m2. How much will it cost to buy the paint?

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6. A can of soda has the shape of a cylinder. The radius of the base measures 4cm andthe height of the can is 10cm. Work out the volume of this cylinder, leaving your

answer in terms of 𝜋.

………………………………………………………………………………………………………………………………………………………………..

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7. This semi-circle has diameter of 20cm.

Show that the perimeter of this semi-circle is 10 (π + 2) cm.

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35

8. Ellis has a container in the shape of a cuboid.

He wants to paint all of the faces of the container except for the base.

Each tin of paint covers 15m2 of space.

How many tins should he buy?

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9. Calculate the shaded area. Leave your answer in terms of 𝜋.

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10. A cube has volume 64cm3. Find the surface area of the cube.

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36

Apply

Apply what you have revised about probability.

You may use a calculator.

Remember

It is important that you remember the formulae for calculating the area of different shapes:

Rectangle and parallelogram = base x perpendicular height

Triangle = (base x perpendicular height) ÷ 2 – it is a very common error to forget to half this!

Circles: area = πr2 and circumference = πd – don’t muddle up the radius and diameter – the

diameter is the long one as it is the longer word!

Trapezium = 1/2 (top + bottom) × height

Don’t forget your units and whether they are squared (area) or cubed (volume)

For composite shapes, split them up on the drawing and check your lengths very carefully.

For surface area write out the area of each face first before adding them all together – check you have all of the sides.

1. Barbara has a rectangular garden with 2 circular ponds. She wants to put a small fencearound the edge of the garden and around both ponds. Work out the length offencing that she needs to buy. Give your answer to 1 d.p.

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37

2. You empty a full cuboid of water which measures 7cm by 5cm by 3cm into anothercuboid which measures 3cm by 2cm by 22cm and is oriented as shown in thediagram. How far up the second cuboid does the water reach?

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3. A tunnel 200m long is dug. The cross-section is made up of a rectangle and a semi-circle. What is the volume of the tunnel?

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4. The volume decreases by 5% when ice melts into water. Tina has an ice cube witheach side measuring 3cm. What will be the volume of water when it melts?

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5. Find the volume of this cylinder. Give your answer correct to the nearest wholenumber.

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6. A can has the shape of a cylinder. There is a label on the can which is 6.5cm high. Itneeds to be 1cm extra length so that it can be glued. Work out the area of the label incm2.

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7. Find the volume of this prism:

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8. Find the shaded area:

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9. The diagram shows two boxes that are both the shapes of cuboids. How many of thelittle boxes fit into the bigger box?

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10. A racing track has the following shape:

It consists of two semi-circles and two straight lines. Each line is 75m long. The total

perimeter is 400m long. Find the distance across the track, marked 𝑥. Give your

answer correct to 2 d.p.

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