MODULE 8 WORKBOOK

MODULE 8 WORKBOOKPerimeter, Area and Volume

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7 May 2019

Module 8

Perimeter, area and volume

The following pods will be needed for the four lessons in Module 8:

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

6. Other 3D Shapes | MATHS-33-008

7. Parts of Circles | MATHS-33-005

Lesson 1

Basic Area and Perimeter

1. Triangles | MATHS-33-001

2. Quadrilaterals | MATHS-33-002

3. Circles | MATHS-33-004

Watch the pod and answer the following questions.

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

d) cm3

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

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

a) 28cm

b) 28cm2

c) 11cm2

d) 22cm

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

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

a) 42m

b) 104cm2

c) 104cm

d) 42cm

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

4. What is the area of this shape?

a) 84cm2

b) 44cm2

c) 42cm2

d) 19cm2

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

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

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

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

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

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

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

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

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

a) 45cm2

b) 36cm2

c) 22.5cm2

d) 90cm2

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

a) 13cm2

b) 20cm2

c) 36cm2

d) 22cm2

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

Practise

Practise basic area and perimeter.

Do not use a calculator.

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

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

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

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

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

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

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

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

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

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

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.

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

Practise

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.

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

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

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

3. Tom has a rectangular lawn measuring 41m by 37m. He wants to put weed killer downall over the lawn. The box says that it covers 60m2 of the lawn. How many boxesshould he buy?

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

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.

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

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.

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

Lesson 2

Compound Area and Perimeter

4. Composite Shapes | MATHS-33-003

1. Find the value of x.

b) 13m

d) 11m

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

2. Find the value of y.

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

3. What is the perimeter of this shape?

a) 60m

b) 65m

c) 72m

d) 74m

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

4. What is the value of x?

a) 14m

b) 13m

c) 12m

d) 11m

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

5. What is the value of y?

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

6. What is the perimeter of this shape?

a) 94m

b) 92m

c) 108m

d) 85m

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

7. Find the perimeter of this shape.

a) 24cm

b) 30cm

c) 48cm

d) 46cm

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

8. Find the area of this shape, in cm2 ,correct to 1 d.p. All lengths are given in cm.

a) 31.4cm2

b) 15.7cm2

c) 157.1cm2

d) 39.3cm2

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

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

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

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

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

Practise

1. Find the area of this shape.

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

2. Find the shaded area.

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

3. Find the area of this compound shape.

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

4. Find the area of this shape.

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

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

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

Practise

1. Find the area of the shape below:

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

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

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

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

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

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

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

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

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

Lesson 3

Volume and Surface Area

5. Prisms | MATHS-33-006

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

c) cm3

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

2. Which of these shapes is NOT a prism?

a) Cube

b) Cuboid

c) Pyramid

d) Cylinder

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

3. Find the volume of this prism.

a) 150cm

b) 150cm2

c) 150cm3

d) 190cm2

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

4. How many faces does this prism have?

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

5. What is the name of this prism?

a) Triangular pyramid

b) Triangular prism

c) Tetrahedron

d) Cuboid

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

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

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

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

a) 21cm3

b) 49cm3

c) 294cm3

d) 343cm3

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

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

a) 54cm2

b) 27cm2

c) 216cm2

d) 9cm2

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

9. What is the volume of this cuboid?

a) 180cm3

b) 120cm3

c) 148cm3

d) 15cm3

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

10. What is the surface area of this cuboid?

a) 105cm3

b) 142cm2

c) 210cm2

d) 156cm2

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

Practise

Practise volume and surface area.

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

2. Find the surface area of this prism.

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

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

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

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

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

5. Find the volume of this trapezoidal prism.

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

Practise

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

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

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

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

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

Lesson 4

Further Length, Area and Volume

6. Other 3D Shapes | MATHS-33-008

7. Parts of Circles | MATHS-33-005

1. Which of the following is a prism?

a) Sphere

b) Cone

c) Cylinder

d) Pyramid

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

2. What is the formula to calculate the volume of the pyramid drawn below?

a) v = l x w x h

b) v= ½ x l x w x h

c) v = 1/3 x l x w x h

d) v = 3 x l x w x h

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

3. Which of the following is NOT the formula for the volume of a sphere?

a) 𝑣 = $%× 𝜋 × 𝑟(

b) 𝑣 = $%× 𝜋 × 𝑟%

c) 𝑣 = $%× 𝜋 × 𝑟 × 𝑟 × 𝑟

d) 𝑣 = $)*+

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

4. Calculate the volume of a sphere with a radius of 3cm, leaving your answer in terms of

a) 108 π cm3

b) 36 π cm3

c) 36 π3 cm3

d) 12 π cm3

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

5. The surface area of a sphere is calculated using the formula A= 4πr2. Use this formula

to calculate the surface area of a sphere with radius 3cm.

a) 113.1cm2

b) 1421.2cm2

c) 28.3cm2

d) 36cm2

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

6. Calculate the area of the sector which has radius 4cm

a) 50.3cm2

b) 15.6cm2

c) 37.7cm2

d) 118.4cm2

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

7. Calculate the area of the sector:

a) 12.6cm2

b) 50.3cm2

c) 157.9cm2

d) 16cm2

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

8. Calculate the perimeter of the sector:

a) 12.6cm

b) 20.6cm

c) 22.3cm

d) 28.6cm

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

9. Which of the following is not the volume of the cone?

a) ,)%𝑐𝑚%

b) 8.38 cm3

c) 26.3 cm3

d) /%× 𝜋 × 8𝑐𝑚%

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

10. Calculate the volume of this shape:

a) 37.7 cm3

b) 763.4 cm3

c) 339.3 cm3

d) 3053.6 cm3

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

Practise

Practise further length, area and volume.

1. Calculate the area of the minor sector AOB, giving

your answer in terms of π.

……………………………………………………………………………………

2. Calculate the perimeter of the minor sector AOB,

leaving your answer in terms of π.

……………………………………………………………………………………

3. Calculate the volume of the pyramid:

……………………………………………………………………………………

4. The diagram shows a hemisphere with a radius = 1cm. Calculate the volume of the

hemisphere, leaving your answer in terms of π.

……………………………………………………………………………………

5. Calculate the volume of the cone, leaving your

answer in terms of π.

……………………………………………………………………………………

Practise

Practise further length, area and volume. You may use a calculator.

1. Calculate the area and perimeter of this sector.

……………………………………………………………………………………

2. Calculate the volume of the cone.

……………………………………………………………………………………

3. The diagram shows a cylinder attached to a hemisphere. Calculate the volume of the entire shape.

……………………………………………………………………………………

4. A cone has a volume of 30π cm3 and a height of 10 cm. Calculate the radius of the

………………………………………………………………………………………………………………………………………………………………

5. The sector of a circle is shown.

Jane calculates the perimeter of the sector as follows:

Perimeter = /2(%32

× 𝜋 × 2 × 8

= 102360

× 𝜋 × 16

= 14.2𝑐𝑚

Is Jane correct? You must give reasons for your answer.

………………………………………………………………………………………………………………………………………………………………

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

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 halve when working with this formula!

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 faces.

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.

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

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

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

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

answer in terms of𝜋.

Area = 𝜋𝑟(

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

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

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

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?

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

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

answer in terms of 𝜋.

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

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

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

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

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?

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

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

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

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

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

Apply what you have revised about probability.

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 halve when working with this formula!

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 faces.

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.

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

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

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

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? Give your answer correct to 2 decimal places.

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

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

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

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

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

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.

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

7. Find the volume of this prism:

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

8. Find the shaded area:

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

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

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

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.

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

Answer Keys

Please refer to workbook for question content

Module 8

Perimeter, Area and Volume

Lesson 1

Basic Area and Perimeter

1. c) m2

2. b) 28cm2

3. d) 42cm

4. c) 42cm2

5. c) 50.27cm2

6. d) 18.8cm

7. a) 25.1cm

8. b) 12cm

9. a) 45cm2

10. d) 22cm2

Practise (Non-Calculator)

1. a) 12 + y + 12 + y = 24 + 2yb) 24 + 2y = 34

2y = 10y = 5

2. To work out the area: 20 x width = 160

Solve 160 ÷ 20 = 8cm

3. Area = π x 11 x 11 = 121π cm2

4. (8 + 4) x height ÷ 2 = 24

12 x height = 48

Height = 4cm

5. Area of triangle = ½ x 8 x 9 = 36

Area of square = 36

Side of square = √36 = 6cm

Practise (Calculator)

1. We need the circumference here so π x 45 = 141.371669

It will rotate 24 times and 24 x 141.371669 = 3392.92cm

The question wants the answer to be in metres so divide by 100 = 33.93m

2. Circumference of the whole circle = π x 10 = 31.416

Half the circumference = 15.71

Need to add the base as perimeter is all the way round

25.71cm

3. Area of lawn = 1517m2

Weed killer: 1517 ÷ 60 = 25.28

Tom needs to buy 26 boxes

4. 54.7 ÷ 9.1 = 6.01cm

5. π x 7.1 = 22.3cm

Lesson 2

Compound Area and Perimeter

1. c) 9m

2. c) 3m

3. c) 72m

4. d) 11m

5. c) 7m

6. a) 94m

7. c) 48cm

8. d) 39.3cm2

9. b) 9cm

10. a) Rectangle and a trapezium

Practise (Non-calculator)

1. Missing sides: 4 – 2 = 2 and 8 – 5 = 3

Area 1 = 8 x 2 = 16

Area 2 = 2 x 5 = 10

Total = 16 + 10 = 26cm2

2. Area of big rectangle = 8 x 10 = 80

Area of small rectangle = 3 x 4 = 12

Shaded area = 80 – 12 = 68 units2

3. Area of rectangle = 6 x 8 = 48

Area of trapezium = (4 + 8) x 5 ÷ 2 = 30

Total area = 48 + 30 = 78 units2

4. Easiest way of doing this one is to subtract the area of the white rectangle from the

area of the pink and white rectangles combined.

Pink rectangle = 6 x 14 = 84

White rectangle = 8 x 4 = 32

Shaded area = 84 – 32 = 52 units2

5. Length of one rectangle = (39 – 6 – 6) ÷ 3 = 9cm

One rectangle = 9 x 6 = 54 cm2

Five rectangles = 54 x 5 = 270cm2

1. Split into 3 rectangles

x = 26 – 10 – 7 = 9

y + 14 = 17 + 13 y = 16

Area 1 = 17 x 9 = 153

Area 2 = 10 x 30 = 300

Area 3 = 7 x 16 = 112

Total = 565 units2

2. Area of rectangle = 8 x 16 = 128

Base of triangles = (16-6)/2 = 5

Area of one triangle = 3 x 5 ÷ 2 = 7.5

Total = 128 + 7.5 + 7.5 = 143cm2

3. Area of rectangle = 8 x 11 = 88m2

Area of trapezium = (2 + 4) x 5 ÷ 2 = 15m2

Area of shaded = 88 – 15 = 73m2

4. Circumference of circle = π x 3 = 9.425cm

Halve it for the semi-circle = 4.712cm

Perimeter = 4.712 + 7 + 7 + 3 = 21.7cm

(Note – remember that you do not have to include the right hand side of the

rectangle, as it does not form an external length)

5. Area of rectangle = 7 x 3 = 21 cm2

Area of semi-circle = π x 1.52 ÷ 2 = 3.53cm2

Total area = 21 + 3.53 = 24.53 cm2

Lesson 3

Volume and Surface Area

1. a) m2

2. c) Pyramid

3. c) 150cm3

4. c) 5

5. b) Triangular prism

6. a) 967.5cm3

7. d) 343cm3

8. a) 54cm2

9. b) 120cm3

10. b) 142cm2

1. Area of the cross section = 3 x 4 ÷ 2 = 6

Volume = 6 x 7 = 42cm3

2. Front: 3 x 4 ÷ 2 = 6

Back: 3 x 4 ÷ 2 = 6

Side: 3 x 7 = 21

Base: 4 x 7 = 28

Top: 5 x 7 = 35

Total = 96cm2

3. Front and back: 4 x 2 x 2 = 16cm2

Top and bottom: 4 x 9 x 2 =72cm2

Side and side: 2 x 9 x 2 =36cm2

Total = 124cm2

4. Volume = area of circle x height

π x 32 x 8 = 72π cm3

5. Volume = area of trapezium x length

Area of trapezium = (3 + 12) x 4 ÷ 2 = 30cm2

Volume of prism = 30 x 10 = 300cm3

1. Front and back: 22 x 2.9 x 2 = 127.6cm2

Side and side: 22 x 2 x 2 = 88cm2

Top and bottom: 2.9 x 2 x 2 = 11.6cm2

Total = 227.2cm2

2. Circle on the top = π x 32 = 28.274cm2

Circle on the bottom = π x 32 = 28.274cm2

The curved surface area is the circumference x height (a rectangle).

Curved surface area = π x 6 x 11 = 207.345cm2

Total = 263.89cm2

3. Trapezium = (9 + 3) x 4 ÷ 2 = 24cm2

Trapezium at back = (9 + 3) x 4 ÷ 2 = 24cm2

Rectangles 5 x 15 = 75cm2

3 x 15 = 45cm2

5 x 15 = 75cm2

9 x 15 = 135cm2

Total = 378cm2

4. Area of front face is made of two rectangles, both 9cm by 2cm

Area of front face = 9 x 2 + 9 x 2 = 36cm2

Volume of prism = 36 x 8 = 288cm3

5. Volume = 4 x 6 x height = 168cm3

Height = 168 ÷ 4 ÷ 6 = 7cm

Lesson 4

Further Length, Area and Volume

1. c) Cylinder

2. c) v = 1/3 x l x w x h

3. a) v = $%× π × r)

4. b) 36 π cm3

5. a) 113.1 cm2

6. c) 37.7 cm2

7. b) 50.3 cm2

8. d) 28.6cm

9. c) 26.3 cm3

10. d) 3053.6 cm3

1. Area = *)+%,+

× 𝜋 × 4) = *%× 16𝜋 = *,

%𝜋𝑐𝑚)

2. Perimeter = *)+%,+

× 𝜋 × 8 + 4 + 4

= 6%𝜋 + 8𝑐𝑚

3. Volume = 1/3 x base area x height

= 1/3 x 100 x 18

= 600 cm^3

4. Volume =

%𝜋𝑐𝑚%

5. Volume = *%× 3) × 𝜋 × 11

=13× 99 × 𝜋

= 33𝜋𝑐𝑚%

1. Area = ,+%,+

× 𝜋 × 8) = 33.5𝑐𝑚)

Perimeter = ,+%,+

× 𝜋 × 16 + 16 = 24.4𝑐𝑚

2. Volume = *%× 𝜋 × 8) × 15 = 1005.3𝑐𝑚%

3. Volume of cylinder = 𝜋𝑟)ℎ = 𝜋 × 3) × 7 = 63𝜋

Volume of hemisphere = $,× 𝜋 × 𝑟% = $

,× 𝜋 × 3% = 18𝜋

Total volume = 63π + 18 π = 81 π cm3

81 π = 254.5cm3

4. Volume of a cone = *%× 𝜋 × 𝑟) × ℎ

30𝜋 = 13× 𝜋 × 𝑟) × 10

30 = 13× 𝑟) × 10

90 = 𝑟) × 10

9 = 𝑟)

3𝑐𝑚 = 𝑟

5. No, Jane is not correct.

Jane has correctly calculated the arc length of the sector though she has not foundthe entire perimeter.

Jane must add on the value of 2xradius = 16cm.

Correct answer: Perimeter = 30.2cm.

Apply (Non-Calculator)

1. Estimate, so round everything.

Rectangle = 10 x 20 = 200m2

Radius of circle = 1.05, round to 1 significant figure = 1

Estimate 𝜋 ≈ 3

Circle area = 𝜋𝑟) =3 x 12 = 3

Grass = 200 – 3 – 3 = 194 m2

2. Area of triangle = (FGHI×JIKLJM))

Area = 6 x 4 ÷ 2 = 12 cm2

75% = 12 ÷ 4 x 3 = 9 cm2

3. Area = πr2

= π x 9 x 9 = 81π cm2

4. Area of triangle = (FGHI×JIKLJM))

= 4 x 5÷ 2 = 10cm2

Volume = 10 x 10 = 100cm3

5. Area of trapezium = (5 + 6) x 8 ÷ 2 = 44 cm2

44 ÷ 4 = 11She needs 11 cans4.70 x 11 = £51.70

6. Volume of cylinder = π x 42 x 10 = 160π cm3

7. Circumference of whole circle = π x 20

Curved part of the semi-circle = π x 20 ÷ 2 = 10π

Add on the bottom side = 10π + 20

Factorise = 10 (π + 2)

8. Surface area to be painted:

Front and back: 9 x 5 x 2 = 90 m2

Left and right: 2 x 5 x 2 = 20 m2

Top = 9 x 2 = 18 m2

Total = 128 m2

128 ÷ 15 = 8 remainder 8

15 goes into 128 8 times plus 8 left over.

Therefore, he needs to buy 9 tins of paint

9. Circle = π x 52 = 25π

Semi-circle = (π x 22 ) / 2 = 4 π ÷ 2 = 2π

Shaded area = 25π – 2π = 23π cm2

10. Each side = √648 = 4

Area of each side = 4 x 4 = 16 cm2

Total surface area = 16 cm2 x 6 = 96cm2

Apply (Calculator)

1. Perimeter of rectangle = 7.9 x 2 + 18.3 x 2 = 52.4m

Circumference of one circle = π x 3.2 = 10.053

Total length of fencing needed = 52.4 + 10.053 + 10.053 = 72.5m

2. Volume of first cuboid = 7 x 5 x 3 = 105cm3

For second cuboid = 105 = 3 x 2 x height

Height = 105 ÷ 6 = 17.5cm

3. Rectangle = 8 x 10 = 80m2

Semi-circle = π x 5 x 5 ÷ 2= 39.2699m2

Total = 119.2699 m2

Volume = 119.2699 x 200 = 23853.98m3

4. Volume of ice cube = 3 x 3 x 3 = 27cm3

5% of 27 = 1.35

New volume = 27 – 1.35 = 25.65cm3

5. π x 62 x 15 = 1696cm3

6. Length of label = circumference of can + 1cm overlap

= π x 7 + 1 = 22.99cm

Area = 22.99 x 6.5 = 149.4cm2

7. Area of cross-section 8 x 2 + 4 x 2 = 24 cm2

Volume 24 x 11 = 264cm3

8. Easiest way is to find the area of the rectangle and then subtract the trapezium area.

Rectangle = 12 x 8 = 96 cm2

Trapezium = (12 + 7) x 3.5 ÷ 2 = 33.25 cm2

Shaded area = 96 – 33.25 = 62.75cm2

9. Up the side 20 ÷ 5 = 4

Along the bottom 12 ÷ 2 = 6

Across the box 9 ÷ 3 = 3

So 3 x 6 x 4 boxes fit = 72 boxes

10. 400 – 75 – 75 = 250m

This is the circumference of a full circle as there are two semi-circles.

π x diameter = 250m

x = 79.58m

MODULE 8 WORKBOOK

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