Functional Skills: Using Length, Area and Volume in Calculations

FS Level 1FS Level 2AQACity & GuildsEdexcelHighfield QualificationsNCFEOpen Awards

Functional Skills: Using Length, Area and Volume in Calculations Revision

Using Length, Area and Volume in Calculations

Often you will be required to use your knowledge of length and areas of shapes to solve a larger problem.

These questions will usually be based around real world scenarios, and may involve multiple steps to reach a solution.

Make sure you are happy with the following topics before continuing.

FS Level 2AQAEdexcelCity & GuildsNCFEOpen AwardsHighfield Qualifications

Question - How do I improve my chances of passing the level 2 maths exam?

Answer – Pre-assessment. This useful tool identifies the key areas of the exam you will need to work on in order to pass your level 2 exam for the first time. 

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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}

FS Level 2AQAEdexcelCity & GuildsNCFEOpen AwardsHighfield Qualifications

The best way to start your level 2 maths revision is…...

The pre-assessment. This covers key areas from the level 2 maths exam and once completed will provide revision suggestions so you know what topics to focus on. 

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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]

Firstly, we need to calculate the volume of the pond.

We know that the pond is in a cylindrical shape, as the base of the pond is circular.

So to find the volume of the pond we need to find the area of the base.

Area =3.14 \times \left(\dfrac{6.1}{2} \right)^2=29.20985 m^2

Now we can calculate the volume of the pond by multiplying the area of the base by the depth of the pond.

Volume =29.20985\times 1.2=\textcolor{orange}{35.05182 \text{ m}^3}

Finally to work out the maximum number of koi Lauren can have in the pond we divide the volume of the pond by the volume of water each koi needs.

\dfrac{35.05182}{1.3}=26.9629...

Therefore, the maximum number of koi Lauren can put in the pond is \textcolor{blue}{26}

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Example 3:

Ralf needs to fill in a hole in the ground that is 0.8 m deep, 1.2 m wide and 3 m long with concrete.

Concrete costs £75 per 0.5 m^3. How much would it cost Ralf to fill in the hole with concrete?

[3 marks]

Firstly, find the volume of the hole:

Volume = 0.8 \times 1.2 \times 3 = \textcolor{purple}{2.88 \text{ m}^3}

Then, divide the volume of the hole by the volume of the concrete, to find how many times greater the volume of the hole is:

2.88 \div 0.5 = 5.76

Finally, multiply this number by the cost of concrete per 0.5 m^3 to find the total cost:

5.76 \times £75 = \textcolor{red}{£432}

FS Level 1FS Level 2AQAEdexcelCity & GuildsNCFEOpen AwardsHighfield Qualifications

Functional Skills: Using Length, Area and Volume in Calculations Example Questions

Firstly, we need to work out the area of the wall.

Area = 5.5\times2.4=13.2 m^2

As Darren is going to paint his wall 3 times, he need to buy enough paint that will cover 13.2\times3=39.6 m^2.

1 litre of paint covers 6.2 m^2.

So he will need \dfrac{39.6}{6.2}=6.387... litres of paint.

Therefore he will need to buy 3 tins of paint because each tin contains 3 litres.

Thus, the total cost = 3\times £16.95=£50.85

We first need to work out the area of the swimming pool.

To do so we need to find the area of the base of the pool. The pool has a diameter of 10.5 m, so it has a radius of 5.25 m. So the area of the base = 3.14\times 5.25^2=86.54625 m^2

Therefore, the volume of the swimming pool = 86.54625 \times 1.5 =129.819375 m^3

To calculate how long it will take Karl to fill his swimming pool we need to divide the volume of the swimming pool by the flow rate of the hose pipe.

Time taken to fill pool =\dfrac{129.819375}{0.068}=1909 minutes to the nearest minute.

First calculate the volume of the brick wall:

Volume =1.2\times0.3\times11.5=4.14 m^3

So multiplying this by 500 will give us the number of bricks she needs.

Number of bricks = 4.14\times500=2070 bricks.

Additional Resources

PFS

Exam Tips Cheat Sheet

FS Level 2
PFS

Formula Booklet

FS Level 2

Functional Skills: Using Length, Area and Volume in Calculations Worksheet and Example Questions

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Using Length, Area and Volume in Calculations L1

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Using Length, Area and Volume in Calculations L2

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