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Geometry and measuresFoundation and Higher

Circles GCSE questions with answers

8 circles questions to try, each with the answer and the full working one tap away. Every question here was made and worked out by the Show Working maths engine, not typed in by hand.

Circle questions ask for the area and circumference of a circle, answers in terms of π, arcs and sectors, and shapes made from semicircles and quarter circles. Use the π button and only round at the end.

Quiz yourself: 8 questions

Worked example 1: area and circumference of a circle

A circle has diameter 13 cm. Work out its area. Give your answer to 1 decimal place.

13 cm
Not drawn accurately

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  1. The radius is half the diameter: 13 ÷ 2 = 6.5 cm.
  2. Area of a circle = π × r².
  3. π × 6.5² = π × 42.25 = 132.7323…
  4. To 1 decimal place: 132.7 cm².

Answer 132.7 cm²

01 / Quiz yourselfTry it, then tap to check

Circles questions to try

Work each one out on paper first. Then open the answer and compare your working with ours, step by step.

01 / Area and circumference of a circleBoth tiers

A circle has radius 15 cm. Work out its area. Give your answer to 1 decimal place.

15 cm
Not drawn accurately

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Show the answer and working
  1. Area of a circle = π × r².
  2. π × 15² = π × 225 = 706.8583…
  3. To 1 decimal place: 706.9 cm².

Answer 706.9 cm²

02 / Area and circumference of a circleBoth tiers

A circle has diameter 20 m. Work out its area. Give your answer to 1 decimal place.

20 m
Not drawn accurately

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Show the answer and working
  1. The radius is half the diameter: 20 ÷ 2 = 10 m.
  2. Area of a circle = π × r².
  3. π × 10² = π × 100 = 314.1593…
  4. To 1 decimal place: 314.2 m².

Answer 314.2 m²

03 / Circles in terms of πBoth tiers

A circle has diameter 18 cm. Work out its circumference. Give your answer in terms of π.

18 cm
Not drawn accurately
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  1. Circumference = π × diameter.
  2. π × 18 = 18π cm.
  3. In terms of π means you leave π as it is.

Answer 18π cm

04 / Circles in terms of πBoth tiers

A circle has diameter 12 m. Work out its area. Give your answer in terms of π.

12 m
Not drawn accurately
Show the answer and working
  1. Radius = 12 ÷ 2 = 6 m.
  2. Area = π × r².
  3. π × 6² = 36π m².
  4. In terms of π means you leave π as it is, without working it out as a decimal.

Answer 36π m²

05 / Semicircles, quarter circles and shaded regionsBoth tiers

The shape is made from a rectangle and a semicircle. Work out the perimeter of the shape. Give your answer to 1 decimal place.

9 cm10 cm
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Show the answer and working
  1. Go round the outside: the top, the curved edge, the bottom and the left side. The dashed line is inside the shape, so leave it out.
  2. The curved edge is half of π × 10: 15.7080…
  3. Perimeter = 9 + 15.7080… + 9 + 10 = 43.7080…
  4. To 1 decimal place: 43.7 cm.

Answer 43.7 cm

06 / Semicircles, quarter circles and shaded regionsBoth tiers

The diagram shows a quarter circle with radius 13 m. Work out its perimeter. Give your answer to 1 decimal place.

13 m
Not drawn accurately

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Show the answer and working
  1. The curved edge is a quarter of the circumference: 2 × π × 13 ÷ 4 = 20.4204…
  2. The two straight edges are both radii: 13 + 13 = 26 m.
  3. Perimeter = 20.4204… + 26 = 46.4204…
  4. To 1 decimal place: 46.4 m.

Answer 46.4 m

07 / Arcs and sectorsBoth tiers

The diagram shows a sector of a circle with radius 12 m. Work out the arc length. Give your answer to 1 decimal place.

85°12 m
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  1. The sector is 85/360 of the whole circle.
  2. Arc length = 85/360 × 2 × π × 12 = 17.8024…
  3. To 1 decimal place: 17.8 m.

Answer 17.8 m

08 / Arcs and sectorsBoth tiers

The diagram shows a sector of a circle with radius 6 cm. Work out the area of the sector. Give your answer to 1 decimal place.

150°6 cm
Not drawn accurately

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Show the answer and working
  1. The sector is 150/360 of the whole circle.
  2. Area = 150/360 × π × 6² = 47.1239…
  3. To 1 decimal place: 47.1 cm².

Answer 47.1 cm²

02 / What's covered4 kinds of question

Circles at GCSE and where marks go

  • Area and circumference of a circleBoth tiers
  • Circles in terms of πBoth tiers
  • Semicircles, quarter circles and shaded regionsBoth tiers
  • Arcs and sectorsBoth tiers

Worked example 2: arcs and sectors

The diagram shows a sector of a circle with radius 3 m. Work out the arc length. Give your answer to 1 decimal place.

165°3 m
Not drawn accurately

You can use a calculator for this one.

  1. The sector is 165/360 of the whole circle.
  2. Arc length = 165/360 × 2 × π × 3 = 8.6394…
  3. To 1 decimal place: 8.6 m.

Answer 8.6 m

A common mistake

Putting the diameter into the area formula. Area is πr², so a circle with a diameter of 10 cm has a radius of 5 cm and an area of 25π = 78.5 cm² to 1 decimal place, not 100π.

03 / Practise itiPhone and iPad

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More geometry and measures topics

Angles and bearingsArea and perimeterVolume and surface areaPythagorasTrigonometryConverting unitsSimilar shapesSine and cosine rulesCircle theoremsCongruent trianglesVectorsTransformationsAll GCSE maths topics
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