## Volume  Audio for slide 1 (mp3 |6|KB)
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.  Audio for slide 2 (mp3 |6|KB)
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.  Audio for slide 3 (mp3 |6|KB)

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  Audio for slide 4 (mp3 |6|KB)

### 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.  Audio for slide 5 (mp3 |6|KB)

### 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).  Audio for slide 6 (mp3 |6|KB)

### 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  ### Learning activity

Audio 7 (mp3 |6|KB)

1.   You are landscaping your front yard and have decided to spread topsoil over the lawn area. The topsoil will be an average of 50 mm thick, and needs to cover an area of 7 m by 8.5 m.

How much topsoil will you need?  DimensionsValue
Length in metres8.5
Width in metres7
Thickness in metres0.05
Volume in cubic metres (Length x Width x Thickness)2.975
Audio 8 (mp3 |6|KB)

2.   You also want to put a water feature pond at one end of the yard. The pond will be round, with a diameter of 1.8 metres. The depth will be 200 mm. How much water will the pond hold when it is full?  DimensionsValue
Surface area which is Diameter ÷ 2 x Diameter ÷ 2 x 3.142.543
Depth in metres0.2
Volume in cubic metres which is Surface area x Depth0.509
Volume in litres509 Go to Avoiding errors