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

## 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.

**Example 1:Â **

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}{Â£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.Â Therefore,

Total cost =24 \times Â£2.75 = \textcolor{blue}{Â£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]**

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 Â£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 Â£75 = \textcolor{red}{Â£432}

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

**Question 1: **Darren wants to paint one of his bedroom walls blue.

His wall is rectangular shaped and is 5.5 m wide and has a height of 2.4 m.

Darren is going to give his bedroom wall 3 coats of paint.

1 litre of paint that Darren buys will cover 6.2 m^2 of wall.

The paint comes in 3 litre tins that cost Â£16.95 each.

Calculate how much it will cost Darren to paint is bedroom wall.

**[4 marks]**

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 Â£16.95=Â£50.85

**Question 2: **Karl has bought a swimming pool for his back garden wants to fill it with water.

The swimming pool is circular shape with a diameter of 10.5 m.

It has a constant depth of 1.5 m.

He is going to fill the swimming pool with a hose pipe that will fill the pool with 0.068 m^3 of water per minute.

Calculate to the nearest minute how long it will take Karl to fill his swimming pool with water using this hose pipe.

Use \pi=3.14

**[4 marks]**

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.

**Question 3: **Emily is building a brick wall for her front garden. She wants to build it 1.2 m high, 0.3 m wide and 11.5 m long.

For each 1 m^3 of wall Emily will need 500 bricks.

How many bricks will she need to build her wall?

**[2 marks]**

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.

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

### Using Length, Area and Volume in Calculations L1

FS Level 1NewOfficial PFS### Using Length, Area and Volume in Calculations L2

FS Level 2NewOfficial PFS[responsive-flipbook id=”pfs_pocket_revision_guide_-_sample”]

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