Functional Skills: Using Length, Area and Volume in Calculations

Example 1: 

The diagram shows Chris’ back garden, his patio is in a square shape and his pond is circular.

Chris wants to lay some new turf down in his back garden. The turf costs \textcolor{orange}{£2.75} per square metre and can only be bought in square metres.

Calculate how much it is going to cost Chris to turf his back garden.

Use \pi=3.14

[4 marks]

Using the measurements given we can deduce the required missing lengths to find the area of the grass section of Chris’ back garden.

To calculate the area of the pond we need to find the radius. The radius is half the diameter, so the radius of this pond =\dfrac{1.1}{2}=\textcolor{orange}{0.55 \text{ m}}

So the area of the pond =3.14\times 0.55^2=0.94985 m^2

Splitting the grass area into two rectangles we can work out the area of this section:

Area of grass =2.9\times 8.3 + 0.2 \times 2.3=24.53 m^2

Obviously the pond will not be turfed, so we need to subtract the area of the pond away from the area of the grass to find out how much of his garden will be turfed:

24.53-0.94985=\textcolor{orange}{23.58015 \text{ m}^2}

Finally, to calculate the cost we are told that turf can only be bought in square metres, so we will need 24 m^2 of turf to cover the required area. Therefore,

Total cost =24 \times £2.75 = \textcolor{blue}{£66}

Example 2:

A plan view of a pond is shown, the pond has a diameter of 6.1 m and is circular.

The depth of the pond is 1.2 m

Lauren wants to fill the pond with koi fish.

Each fish must have at least 1.3 m^3 of water.

Calculate the maximum amount of koi fish Lauren can put in her pond.

Use \pi=3.14

[4 marks]