Circles: Circumference and Area
A circle's diameter is twice its radius, and its circumference, the distance around the outside, is found using C = pi x d, or equivalently C = 2 x pi x r, while the area enclosed by a circle is found using A = pi x r^2, where the radius must be squared, not the diameter. Pi, written as the Greek letter or approximated as 3.14, is the fixed ratio between a circle's circumference and its diameter.
Before you start
Make sure you're comfortable with these topics first:
Method
- Identify whether you are given the radius or the diameter, remembering diameter = 2 x radius.
- To find the circumference, use C = pi x d, or C = 2 x pi x r.
- To find the area, use A = pi x r^2, making sure you square the radius rather than the diameter.
- Use the pi button on a calculator for full accuracy, or use pi = 3.14 if the question tells you to approximate.
- For a semicircle or quarter circle, first find the full circle's circumference or area, then divide by 2 or 4, and add any straight edges if you need a perimeter.
- Give your final answer to the accuracy asked for, with the correct unit: cm for length, cm^2 for area.
Worked example
A circle has a radius of 6 cm. Find (a) its circumference, (b) its area. Use pi = 3.14, and give your answers to 1 decimal place.
- Circumference: C = 2 x pi x r = 2 x 3.14 x 6.
- Calculate: 2 x 3.14 = 6.28, then 6.28 x 6 = 37.68, so C = 37.7 cm (1 decimal place).
- Area: A = pi x r^2 = 3.14 x 6^2.
- Calculate: 6^2 = 36, then 3.14 x 36 = 113.04, so A = 113.0 cm^2 (1 decimal place).
Practice questions
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Q1Find the circumference of a circle with radius 5 cm, using pi = 3.14.Show answer
Answer: 2 x 3.14 x 5 = 31.4 cm
Q2Find the area of a circle with radius 4 cm, using pi = 3.14.Show answer
Answer: 3.14 x 16 = 50.24, so approximately 50.2 cm^2
Q3A circle has a diameter of 10 cm. Find its circumference, using pi = 3.14.Show answer
Answer: 3.14 x 10 = 31.4 cm
Q4A circle has a diameter of 8 cm. Find its area, using pi = 3.14.Show answer
Answer: Radius = 4 cm, so area = 3.14 x 16 = 50.24, approximately 50.2 cm^2
Q5A circle has a circumference of 62.8 cm. Using pi = 3.14, find its radius.Show answer
Answer: 62.8 = 6.28 x r, so r = 62.8 / 6.28 = 10 cm
Q6Find the area of a semicircle with radius 6 cm, using pi = 3.14.Show answer
Answer: Full circle area = 3.14 x 36 = 113.04, so semicircle area = 113.04 / 2 = 56.52, approximately 56.5 cm^2
Q7A circular pond has a radius of 3.5 m. Find its circumference to 1 decimal place, using pi = 3.14.Show answer
Answer: 2 x 3.14 x 3.5 = 21.98, which rounds to 22.0 m
Q8Find the perimeter of a semicircle with radius 7 cm (the curved edge plus the straight diameter edge), using pi = 3.14.Show answer
Answer: Curved edge = 3.14 x 7 = 21.98 cm, diameter = 14 cm, so perimeter = 21.98 + 14 = 35.98, approximately 36.0 cm
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
A circle has a radius of 9 cm. Work out its area, using pi = 3.14 and giving your answer to 1 decimal place.
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A running track has two straight sections and two semicircular ends. Each straight section is 80 m long, and each semicircular end has a radius of 20 m. (a) Work out the total length of the two semicircular ends together (this equals the circumference of one full circle of radius 20 m). (b) Work out the total distance around the whole track. Use pi = 3.14.
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Free printable worksheet
Want more practice on paper? Download the circles: circumference and area worksheet pack - 8 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 11 of KS3 Maths Workbook 2, the whole course as one free printable PDF.
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