1

WJEC MATHEMATICS

INTERMEDIATE

SHAPE AND AREA

VOLUME

2

Contents

Volume of basic shapes

Capacity

Finding the depth

Credits

WJEC Question bank

http://www.wjec.co.uk/question-bank/question-search.html

3

Volume of basic shapes

The volume of a 3D shape is the amount of space taken up by the

shape. The units will be cubic (e.g. cm3, mm3, litres, ml, etc.)

Counting cubes

The easiest way to calculate volume is to count the cube that an

object is made from.

The easiest way to count all the small cubes would be to count how

many cubes make the front face and then multiply it by two (The

shape is 2 layers deep)

Number of cubes on the front face = 47

So total cubes = 47 x 2 = 94

You may require units on your answer. If you are told each

square is 1cm3, then this answer would be 94cm3

4

Volume of Prisms

A prism is a three dimensional solid with uniform cross section. (it

looks like one shape that has been stretched backwards). Here are

examples of prisms.

More commonly for cuboids, we say

VOLUME = LENGTH WIDTH HEIGHT

Examples

VOLUME = AREA OF CROSS SECTION LENGTH

Think of this as the 'front

face'

5

Exercise G15

Calculate the volume of the following shapes

1.

2.

3.

6

4.

5.

7

6.

7.

8

Capacity

Often, volume questions include units. Two important conversions

that you should know are;

Example

Find the volume of the cuboid in litres

To convert from to ,

8.

9.

9

Exercise G16

Find the volume of the following shapes in litres

Finding the depth

For some questions, you will be given the volume but not the depth.

For these questions, you will need to form and solve an equation.

Example

1.8 litres of water is poured into the following container. How high is

the water level?

86cm

59cm 2.1m

64cm

5.1m

30cm

5cm

We need to form an equation and then

solve it.

[Remember 1.8 litres = 1800cm3]

1. 2.

10

Exercise G17

2.4 litres of water is poured into the following container. Calculate the

depth of the water.

Exam Questions G26

30cm

20cm

1.

2.

11

3.

4.

12

5.