Unit 22 Section 2 : Volume of a Cube

In this section we introduce the volume of a cube and some other units of volume.

The volume of a cube
 Volume of a cube = a × a × a = a³ where a is the length of each side of the cube.

Example
We want to find the volume of this cube in m³ and cm³.

To find the volume in m³, we calculate 2 m × 2 m × 2 m.
The volume of the cube is 8 m³ (8 cubic metres).

To find the volume in cm³, we need to remember that 2 m = 200 cm and calculate 200 cm × 200 cm × 200 cm.
The volume of the cube is 8 000 000 cm³ (eight million cubic centimetres).

Practice Question
Work out the answer to this question then click to see whether you are correct.
What is the volume of this cube in cm³?

Exercises

Work out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on to see the answer.

Question 1
Work out the volume of each of the cubes below. Give your answers as decimals where necessary.
 (a) m³ (b) cm³ (c) cm³ (d) m³

Question 2
A large box is a cube with sides of length 80 cm. Smaller boxes, which are also cubes, have sides of length 20 cm.

(a) What is the volume of the larger box?
cm³

(b) What is the volume of the smaller box?
cm³

(c) How many small boxes will fit in the large box?
small boxes

Question 3
A cube has sides of length ½ m. Calculate the volume of the cube:

 m³

cm³

Question 4
The diagram below shows a cube with sides of length 30 cm.
A smaller cube with sides of length 5 cm has been cut out of the larger cube.
 (a) What is the volume of the large cube before the small cube is cut out? cm³ (b) What is the volume of the small cube? cm³ (c) What is the volume of the shape that is left? cm³

Question 5
Wooden building blocks are cubes with sides of length 4 cm. A child builds a tower using 6 blocks.

What is the volume of the tower?
cm³

Question 6
The 'staircase' below is built from wooden cubes with sides of length 6 cm.
 (a) What is the volume of the staircase? cm³ (b) A similar staircase is 4 blocks high instead of 3.What is the volume of this staircase? cm³

Question 7
A cube has volume 343 cm³.

(a) How long are the sides of the cube?
cm

(b) What is the area of one face of the cube?
cm²

(c) What is the total area of the surface of the cube?
cm²

Question 8
The area of one face of a cube is 81 cm².

What is the volume of the cube?
cm³

You have now completed Unit 22 Section 2
 Your overall score for this section is Correct Answers You answered questions correctly out of the questions in this section. Incorrect Answers There were questions where you used the Tell Me button. There were questions with wrong answers. There were questions you didn't attempt.
 Since these pages are under development, we find any feedback extremely valuable. Click here to fill out a very short form which allows you make comments about the page, or simply confirm that everything works correctly.