Robinson Tuition
Grade 6 · Higher · free GCSE maths worksheet

Arc length and sector area

Fractions of a circle.

13 original questions, 43 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

A sector of a circle has radius 7.5 cm and angle 140°.

  1. Work out the arc length of the sector.
  2. Work out the area of the sector.

Give each answer correct to 3 significant figures.

4 marks
Show answer
a) 18.3 cm b) 68.7 cm²
2

A sector of a circle has radius 6 cm and area 15π cm².

Work out the angle of the sector.

2 marks
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150°
3

A sector of a circle has radius 9 cm and angle 120°.

Work out the arc length of the sector.

Give your answer in terms of π.

2 marks
Show answer
6π cm
4

A sector of a circle has radius 5 cm.

The arc length of the sector is 8.4 cm.

Find the angle of the sector.

Give your answer correct to 1 decimal place.

3 marks
Show answer
96.3°
5

A sector of a circle has radius 6 cm.

The perimeter of the sector is 42 cm.

The angle of the sector is reflex.

Work out the angle of the sector.

Give your answer correct to 1 decimal place.

3 marks
Show answer
286.5°
6
  1. A quarter circle has radius 10 cm. Work out its area. Give your answer in terms of π.
  2. A semicircle has diameter 14 cm. Work out its area. Give your answer in terms of π.
3 marks
Show answer
a) 25π cm² b) 24.5π cm²
7

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
8

A sector of a circle has angle 120° and area 48π cm².

Work out the perimeter of the sector.

Give your answer correct to 3 significant figures.

4 marks
Show answer
49.1 cm
9

A sector of a circle has radius 8 cm and angle 75°.

Work out the perimeter of the sector.

Give your answer correct to 3 significant figures.

3 marks
Show answer
26.5 cm
10

A lawn is in the shape of a sector of a circle with radius 6 m and angle 210°.

A gardener puts edging all the way round the edge of the lawn.

Work out the length of edging needed.

Give your answer correct to 3 significant figures.

3 marks
Show answer
34.0 m
11

OAB is a sector of a circle, centre O, with radius 10 cm and angle AOB = 60°.

The chord AB divides the sector into a triangle and a segment.

Calculate the area of the segment.

Give your answer correct to 3 significant figures.

10 cm60°OABDiagram NOT accurately drawn
4 marks
Show answer
9.06 cm²
12

A sector of a circle has angle 100°.

The arc length of the sector is 5π cm.

Find the radius of the sector.

3 marks
Show answer
9 cm
13

A sector of a circle has radius x cm and angle 144°.

A circle has radius 6 cm.

The area of the sector is equal to the area of the circle.

Work out the value of x.

Give your answer in the form k√10.

5 marks
Show answer
x = 3√10

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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