Functional Skills: Circles

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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 (Ï€)(pi). Ï€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 (Ï€=3.141592654…)(pi = 3.141592654…)

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

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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.

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Area and Circumference 

Area of a circle =Ï€r2= pi r^2

Circumference of a circle =Ï€d=2Ï€r=pi d = 2pi r

r=r= radius and d=d= diameter 

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Example 1: Calculating Area

Calculate the area of the circle shown on the right with a diameter of 4.84.8 cm to 11 decimal place.

Use π=3.14pi = 3.14

[3 marks]

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

radius =4.82=2.4=dfrac{4.8}{2}=2.4 cm

We know that the area of a circle =Ï€r2=pi r^2

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

area of the circle = 3.14×2.42=18.13.14 times 2.4^2=textcolor{orange}{18.1} cm2^2 (11 dp)

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Example 2: Calculating Circumference

Calculate the circumference of the circle shown on the right with a radius of 2.92.9 cm to 11 decimal place.

Use π=3.14pi = 3.14

[2 marks]

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

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

circumference of the circle =2×3.14×2.9=18.2=2 times 3.14 times 2.9=textcolor{orange}{18.2} cm (11 dp)

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Functional Skills: Circles Example Questions

Question 1: The circle below has a radius of 8.68.6 cm.

a) Calculate the circumference of the circle to 22 decimal places.

[2 marks]

b) Calculate the area of the circle to 22 decimal places.

[2 marks]

Use π=3.14pi=3.14

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a) Circumference = 2×π×r2times pi times r

Circumference of the circle = 2×3.14×8.6=54.012times 3.14times 8.6=54.01 cm to 22 decimal places.

 

b) Area = πr2pi r^2

Area of the circle = 3.14×8.62=232.233.14 times 8.6^2=232.23 cm2^2 to 22 decimal places.

Question 2: Calculate the area of the circle below, which has a diameter of 11.311.3 cm.

Give your answer to 22 decimal places and use π=3.14pi=3.14

[2 marks]

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Area = πr2pi r^2

We know that the diameter is double the length of the radius, so r=11.32=5.65r=dfrac{11.3}{2}=5.65 cm

Thus the area of the circle = 3.14×5.652=100.243.14 times 5.65^2=100.24 cm2^2 to 22 decimal places.

Question 3: The circumference of a circle is 11.93211.932 cm. Use π=3.14pi=3.14, to find the area of the circle, giving your answer to 22 decimal places.

[3 marks]

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We know that circumference = 2Ï€r2 pi r

 

So 11.932=2×3.14×r11.932= 2times3.14times r

 

⇒r=11.9322×3.14=1.9rArr r = dfrac{11.932}{2times3.14}=1.9 cm

 

Area = 3.14×1.92=11.343.14 times 1.9^2=11.34 cm2^2 to 22 decimal places.

Question 4: Calculate the circumference of the circle below with diameter of 3.23.2 m, giving your answer correct to 22 decimal places.

Use π=3.14pi =3.14

[2 marks]

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Using circumference = πdpi d

The circumference of the circle = 3.14×3.2=10.053.14 times 3.2=10.05 m to 22 decimal places.

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Specification Points Covered

L2.16 – Calculate perimeters and areas of 2-D shapes including triangles and circles and composite shapes including non-rectangular shapes (formulae given except for triangles and circles)

Functional Skills: Circles Worksheet and Example Questions

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Circles L2

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