Squares, roots and powers
Squares, roots and powers

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

Free course

Squares, roots and powers

1.4 Cubes

To find the cube of a number, multiply three copies of it together. For example:

You can use your calculator to find cubes. 23 is ‘two cubed’ or ‘two to the power three’. Just as ‘square root’ is the opposite process to squaring, so 'cube root' is the opposite process to cubing.

43 = 64, so = 4.

In the same way that square units are used to measure area, cubic units are used to measure volume. A cube measuring 1 cm × 1 cm × 1 cm has a volume of 1 centimetre cubed, or 1 cubic centimetre, written as 1 cm3, or 1 cc. The volume of a ‘box’ is length x width x height, so the volume of this cube (10 mm × 10 mm × 10 mm) in millimetres is

   1 cm3 = 10 mm × 10 mm × 10 mm = 1000 mm3.

Example 5

My half-litre measuring jug is marked off in divisions of 100 ml, with subdivisions of 20 ml. I want to measure out 420 cc, but the only conversion table I have tells me that a litre is one cubic decimetre. (One decimetre is a tenth of a metre.) How many cubic centimetres are there in a litre? Can I use the measuring jug for 420 cc?


There is one cubic decimetre in a litre, so 1 litre measures 1 dm × 1 dm × 1 dm (if shaped into a cube). (Note: 1 m = 10 dm = 100 cm.) There are 10 centimetres in a decimetre, so a 1 litre cube would measure

  10 cm × 10 cm × 10 cm = 1000 cm3.

So 1 litre is 1000 cm3. This is a useful result.

But there are 1000 millilitres in a litre, so it turns out that a millilitre is the same as a cubic centimetre.

  1 ml = 1 cm3.

So I can use the jug to measure 420 ml, or 420 cc (or cm3).

(Note: 1 cubic centimetre can be written as 1 cc or 1 cm3.)


Take your learning further

Making the decision to study can be a big step, which is why you'll want a trusted University. The Open University has 50 years’ experience delivering flexible learning and 170,000 students are studying with us right now. Take a look at all Open University courses.

If you are new to University-level study, we offer two introductory routes to our qualifications. You could either choose to start with an Access module, or a module which allows you to count your previous learning towards an Open University qualification. Read our guide on Where to take your learning next for more information.

Not ready for formal University study? Then browse over 1000 free courses on OpenLearn and sign up to our newsletter to hear about new free courses as they are released.

Every year, thousands of students decide to study with The Open University. With over 120 qualifications, we’ve got the right course for you.

Request an Open University prospectus371