Functional Skills: Circles

FS Level 1FS Level 2AQACity & GuildsEdexcelHighfield QualificationsNCFEOpen Awards

Functional Skills: Circles Revision

Circles

You will need to be able to identify and use properties of circles to then calculate the area and circumference of a circle.

Calculating the area and circumference involve working with a value called pi (\pi). \pi is the ratio of the circle’s circumference to its diameter (you don’t need to remember this) and is a decimal that never ends (\pi = 3.141592654...)

If you calculator has a \pi button then you can use this for calculations. However, you may be told to use \textcolor{orange}{3.14} or \textcolor{orange}{3.142} in place of \pi instead.

FS Level 1AQAEdexcelCity & GuildsNCFEOpen AwardsHighfield Qualifications
FS Level 2AQAEdexcelCity & GuildsNCFEOpen AwardsHighfield Qualifications

See what level 2 maths topics you need support with.

The subject knowledge assessment tests your skills on a number of topics that will come up in the actual exam. You then get feedback on what you need to revise. 

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Properties of Circles

The circumference of a circle is the length around the outside, or in other words – the perimeter.

The centre of a circle is the point exactly in the middle, where the distance to the circumference is equal from any direction.

The diameter of a circle is the distance from one side of the circle to the other, passing through the centre.

The radius of a circle is the distance from the centre to the circumference. The radius is always half of the diameter.

FS Level 1FS Level 2AQAEdexcelCity & GuildsNCFEOpen AwardsHighfield Qualifications

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Area and Circumference 

Area of a circle = \pi r^2

Circumference of a circle =\pi d = 2\pi r

r= radius and d= diameter 

FS Level 2AQAEdexcelCity & GuildsNCFEOpen AwardsHighfield Qualifications
FS Level 2AQAEdexcelCity & GuildsNCFEOpen AwardsHighfield Qualifications

Example 1: Calculating Area

Calculate the area of the circle shown on the right with a diameter of 4.8 cm to 1 decimal place.

Use \pi = 3.14

[3 marks]

The diameter of a circle is double the length of the radius, so

radius =\dfrac{4.8}{2}=2.4 cm

We know that the area of a circle =\pi r^2

Thus, using r=2.4 and \pi =3.14,

area of the circle = 3.14 \times 2.4^2=\textcolor{orange}{18.1} cm^2 (1 dp)

FS Level 2AQAEdexcelCity & GuildsNCFEOpen AwardsHighfield Qualifications

Struggling with Circles?

Take our functional skills maths level 2 assessment and see how you would score in the real exam.

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Example 2: Calculating Circumference

Calculate the circumference of the circle shown on the right with a radius of 2.9 cm to 1 decimal place.

Use \pi = 3.14

[2 marks]

We know that the circumference of a circle = \pi d = 2\pi r

Thus, using r=2.9 and \pi =3.14,

circumference of the circle =2 \times 3.14 \times 2.9=\textcolor{orange}{18.2} cm (1 dp)

FS Level 2AQAEdexcelCity & GuildsNCFEOpen AwardsHighfield Qualifications

Functional Skills: Circles Example Questions

a) Circumference = 2\times \pi \times r

Circumference of the circle = 2\times 3.14\times 8.6=54.01 cm to 2 decimal places.

 

b) Area = \pi r^2

Area of the circle = 3.14 \times 8.6^2=232.23 cm^2 to 2 decimal places.

Area = \pi r^2

We know that the diameter is double the length of the radius, so r=\dfrac{11.3}{2}=5.65 cm

Thus the area of the circle = 3.14 \times 5.65^2=100.24 cm^2 to 2 decimal places.

We know that circumference = 2 \pi r

 

So 11.932= 2\times3.14\times r

 

\rArr r = \dfrac{11.932}{2\times3.14}=1.9 cm

 

Area = 3.14 \times 1.9^2=11.34 cm^2 to 2 decimal places.

Using circumference = \pi d

The circumference of the circle = 3.14 \times 3.2=10.05 m to 2 decimal places.

Additional Resources

PFS

Exam Tips Cheat Sheet

FS Level 2
PFS

Formula Booklet

FS Level 2

Functional Skills: Circles Worksheet and Example Questions

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Circles L2

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