Functional Skills: Circles
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.
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.
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Area and CircumferenceÂ
Area of a circle = \pi r^2
Circumference of a circle =\pi d = 2\pi r
r= radius and d= diameterÂ
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)
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)
Functional Skills: Circles Example Questions
Question 1:Â The circle below has a radius of 8.6 cm.
a)Â Calculate the circumference of the circle to 2 decimal places.
[2 marks]
b) Calculate the area of the circle to 2 decimal places.
[2 marks]
Use \pi=3.14
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.
Question 2:Â Calculate the area of the circle below, which has a diameter of 11.3 cm.
Give your answer to 2 decimal places and use \pi=3.14
[2 marks]
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.
Question 3:Â The circumference of a circle is 11.932 cm. Use \pi=3.14, to find the area of the circle, giving your answer to 2 decimal places.
[3 marks]
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.
Question 4:Â Calculate the circumference of the circle below with diameter of 3.2 m, giving your answer correct to 2 decimal places.
Use \pi =3.14
[2 marks]
Using circumference = \pi d
The circumference of the circle = 3.14 \times 3.2=10.05 m to 2 decimal places.
Functional Skills: Circles Worksheet and Example Questions
Circles L2
FS Level 2NewOfficial PFS[responsive-flipbook id=”pfs_pocket_revision_guide_-_sample”]
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