Cubes and Cube Roots

Arithmetic

Cubes and cube roots

( all measurements will be assumed to be in centimetres )

The volume of the cube shown is 5 5 5 which is 125 cm3.

What is the volume of this cube ?

5cm

3cm

Cubes and cube roots

What are the volumes of the two cubes below ?

8cm

4cm

Cubes and cube roots

Suppose now that you were told the volume of a cube and you were asked to find the length of the side of the cube.

For example , the cube shown has a volume of 216cm3 , what is the length of the side of the cube?

Cubes and cube roots

Find the length of the sides of these cubes

Volume =1000

Volume = 343

Cubes and cube roots

You are going now to use a trial and error method to find the length of the side of the cube. In the diagrams below you will initially guess at the answer and then try to improve on your guess and get a better and better answer for the length of the side of the cube.

Try to find the length of the sides of these cubes

Volume = 200cm3

Volume =75cm3

Try to get your answers correct to 3 decimal places.

Cubes and cube roots

The cube root buttonLook at your calculator and see if you can find

the cube root symbol. It should look like this 3 . You will need to press the MATHS button first

to see it if you are using a graphic calculator.This 3 is called the cube root button. Use it to find 325 345 3105 380 3120 3500

Cubes and cube roots

Your answers should look like those in the diagram shown.

Look back at the answers you got for the sides of the cubes on the previous slide. Do you see how you might use the cube root button to help you find the side of a cube very easily.

Cubes and cube roots

Use the cube root button on your calculator to find the lengths of the sides of the cubes shown.

Volume = 640cm3

Volume = 200cm3

Volume = 400cm3

Volume = 850cm3