## Volume

### 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 cm^{3}

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 m^{3}

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 m^{3} 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 m^{3}

Since there are 1000 litres in 1 m^{3}, the volume in litres is:

3.815 m^{3} 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?

Dimensions | Value |
---|---|

Length in metres | 8.5 |

Width in metres | 7 |

Thickness in metres | 0.05 |

Volume in cubic metres (Length x Width x Thickness) | 2.975 |

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?

Dimensions | Value |
---|---|

Surface area which is Diameter ÷ 2 x Diameter ÷ 2 x 3.14 | 2.543 |

Depth in metres | 0.2 |

Volume in cubic metres which is Surface area x Depth | 0.509 |

Volume in litres | 509 |