So far we've described length as being one dimensional and area as two dimensional.

But for an object to take up space in the real world it needs a third dimension.

Volume is a way of measuring three dimensional space.

We know that if a square measures one metre by one metre, it will have an area of one square metre (m²).

If we now give it a depth of one metre, it will have a volume of one cubic metre (m³).

This is the standard unit of volume in the SI metric system.

Here are some metric volume measurements:

            1 cubic metre (m³) = 1,000 litres (L) = 1,000,000 cubic centimetres (cm³)

            1 L = 1,000 millilitres (mL) = 1,000 cm³

            1 mL = 1 cm³

Example 1: Concrete driveway

How much concrete do you need to order for a driveway that measures 10 m in length, 3 m in width and 150 mm in thickness?

Notice that there is a combination of units here - the length and width are in metres and the thickness is in millimetres. So the first thing we need to do is convert the thickness to metres: 150 mm = 0.150 cm³

Now we can do the calculation, as shown below.

Volume of a rectangular prism = length x width x thickness

            = 10 m x 3 m x 0.15 m

            = 4.5 m³

In practice, you might add 10% to cover variations in the ground level which will affect the thickness of the slab. This means you would add 0.45 m³ to the total.

Example 2: 2-stroke fuel

A common petrol:oil ratio for 2-stroke engines is 25:1. This means that for every 25 parts of petrol you need to mix in 1 part of 2-stroke oil.

If you had a 4 litre container of petrol, how much oil do you need to add?

We know that:

            1 L = 1000 mL, so

            4 L = 4,000 mL.

Therefore the calculation will be as follows.

            4,000 mL (petrol) ÷ 25 = 160 mL (2-stroke oil).

Example 3: Water tank

How much water can a tank hold with a diameter of 1800 mm and a height of 1500 mm?

Here is the calculation.

Cylinder volume = area of circle (cross section) x height

           =   diameter   x   diameter   x   3.14   x   height
                     2                 2

           =   1.8   ÷   2   x   1.8   ÷   2   x   3.14   x   1.5

           =   0.9   x   0.9   x   3.14   x   1.5

           =   3.815 m³

Since there are 1000 litres in 1 m³, the volume in litres is:

           3.815 m³ x 1000 = 3815 L