Robinson Tuition
Year 8 · Key Stage 3 · free KS3 maths worksheet

Area and circumference of circles

12 original questions, 43 marks. Type your answers below for an instant mark and a score (algebra in any equivalent form, e.g. 2sqrt(3) or 2√3), or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

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The questions

1

The diagram shows a circle with centre O.

  1. Write down the mathematical name of the straight line P, which touches the circle at one point.
  2. Write down the mathematical name of the straight line Q.
  3. Write down the mathematical name of the shaded region R.
  4. The radius of a different circle is 4.5 cm. Write down its diameter.
OPQRDiagram NOT accurately drawn
4 marks
Show answer
a) tangent b) chord c) segment d) 9 cm
2

A circular coaster has a diameter of 10 cm.

  1. Work out the circumference of the coaster.
  2. Work out the area of the coaster.

Give each answer correct to 1 decimal place.

3 marks
Show answer
a) 31.4 cm b) 78.5 cm²
3

A circle has diameter 18 cm.

  1. Work out the circumference of the circle. Give your answer in terms of π.
  2. Work out the area of the circle. Give your answer in terms of π.
3 marks
Show answer
a) 18pi cm b) 81pi cm2
4

The circumference of a circle is 14π cm.

Work out the area of the circle. Give your answer in terms of π.

4 marks
Show answer
49π cm²
5
  1. A bicycle wheel has a circumference of 88 cm. Work out its diameter.
  2. A circular rug has an area of 154 cm². Work out its radius.

Give each answer correct to 1 decimal place.

4 marks
Show answer
a) 28.0 cm b) 7.0 cm
6

Shape A is a semicircle with diameter 12 cm. Shape B is a quarter circle with radius 8 cm.

  1. Work out the area and the perimeter of shape A.
  2. Work out the area and the perimeter of shape B.

Give your answers correct to 1 decimal place.

12 cm8 cmABDiagram NOT accurately drawn
4 marks
Show answer
a) area 56.5 cm², perimeter 30.8 cm b) area 50.3 cm², perimeter 28.6 cm
7

A circle of radius 5 cm is drawn inside a square with sides of length 10 cm, so that the circle touches all four sides of the square.

The region inside the square but outside the circle is shaded.

Work out the shaded area. Give your answer correct to 1 decimal place.

10 cm5 cmDiagram NOT accurately drawn
4 marks
Show answer
21.5 cm²
8

The diagram shows a sector of a circle with radius 9 cm and angle 100°.

Work out the area of the sector. Give your answer correct to 1 decimal place.

9 cm100°Diagram NOT accurately drawn
2 marks
Show answer
70.7 cm²
9

A slice of a round cheese is a sector of a circle with radius 12 cm and angle 75°.

  1. Work out the length of the curved edge (the arc) of the slice.
  2. Work out the perimeter of the slice.

Give your answers correct to 1 decimal place.

12 cm75°Diagram NOT accurately drawn
3 marks
Show answer
a) 15.7 cm b) 39.7 cm
10

A circular pond has radius 3 m.

The pond is surrounded by a path of constant width 1 m.

Calculate the area of the path. Give your answer correct to 3 significant figures.

3 m1 mpondpathDiagram NOT accurately drawn
4 marks
Show answer
22.0 m²
11

A sector of a circle has angle 45°.

The arc length of the sector is 3π cm.

Work out the area of the sector.

Give your answer in terms of π.

4 marks
Show answer
18π cm²
12

A school field is a rectangle 100 m long and 60 m wide with a semicircle on each of the two short ends.

  1. Work out the perimeter of the field.
  2. Work out the area of the field.

Give your answers correct to 1 decimal place.

100 m60 mDiagram NOT accurately drawn
4 marks
Show answer
a) 388.5 m b) 8827.4 m²

Your score

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Every question here is original and written by Robinson Tuition. It follows the Key Stage 3 programme of study; Year 9 sheets end with extension questions for top sets.

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