Maths Library

Circumference and Area of Circles: Year 9 maths

This topic covers finding the radius, diameter, circumference, and area of circles and fractional sectors. Students practise using pi formulas, working in terms of pi, and rounding answers to specified degrees of accuracy.

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What this covers

Circumference and Area of Circles is taught in Year 9 (age 13 to 14, KS3) as a main teaching focus. It sits in the Measurement strand.

Worked example

Find the area of a circle with diameter 14 cm. Give your answer to 1 decimal place. Use pi = 3.142.

  1. Find the radius: r = diameter ÷ 2 = 142 = 7 cm.
  2. Apply the area formula: Area = pi × r^2.
  3. Calculate: 3.142 × 7^2 = 3.142 × 49 = 153.958, rounding to 154.0 cm^2.

Answer: 154.0 cm^2

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Finding circumference given diameter or radius using integer values.
  2. Finding area given radius using integer values.
  3. Finding area or circumference given diameter, requiring conversion to radius or selection of correct formula.
  4. Perimeter and area of semicircles and quarter circles.
  5. Reverse problems (finding radius from area/circumference) and shaded region composite problems.

Common mistakes

  • Squaring the diameter instead of the radius when calculating area.
  • Forgetting to add the straight diameter edge when finding the perimeter of a semicircle.

Curriculum links

Indicative matches to National Curriculum for England. Check wording and codes against the official document.

  • Solve problems involving the area and circumference of circles and composite shapes.

Sample sheet and answers

Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.

Circumference and Area of Circles

Year 9 maths

Qs
6
Marks
18
NameDateScore / 18
1.
A circle has radius 12 cm. Find its area. Give your answer to 1 decimal place.
[3]
2.
A circle has radius 5 cm. Find its area. Give your answer to 1 decimal place.
[3]
3.
A circle has radius 7 cm. Find its area. Give your answer to 1 decimal place.
[3]
4.
A circle has radius 6 cm. Find its circumference. Give your answer to 1 decimal place.
[3]
5.
A circle has radius 6 cm. Find its area. Give your answer to 1 decimal place.
[3]
6.
A circle has radius 10 cm. Find its area. Give your answer to 1 decimal place.
[3]

Answer key

  1. 452.4 cm2A = πr2 = π × 122; = 452.4 cm2
  2. 78.5 cm2A = πr2 = π × 52; = 78.5 cm2
  3. 153.9 cm2A = πr2 = π × 72; = 153.9 cm2
  4. 37.7 cmC = 2πr = 2 × π × 6; = 37.7 cm
  5. 113.1 cm2A = πr2 = π × 62; = 113.1 cm2
  6. 314.2 cm2A = πr2 = π × 102; = 314.2 cm2