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Grade 3 · Foundation · free GCSE maths worksheet

Circumference and area of a circle

Using pi, in terms of pi and as decimals.

14 original questions, 58 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 circle has radius 6 cm.

  1. Work out the circumference of the circle. Give your answer correct to 1 decimal place.
  2. Work out the area of the circle. Give your answer correct to 1 decimal place.
3 marks
Show answer
a) 37.7 cm b) 113.1 cm2
2

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
3

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
4

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
5

A rectangle is 15 cm long and 8 cm wide. A circle of radius 3 cm is drawn completely inside the rectangle and is cut out.

The rest of the rectangle is shaded.

Work out the shaded area as a percentage of the area of the rectangle. Give your answer correct to 1 decimal place.

15 cm8 cm3 cmDiagram NOT accurately drawn
4 marks
Show answer
76.4%
6

The diagram shows a square OABC with sides of length 6 cm. A quarter circle, centre O and radius 6 cm, is drawn inside the square from A to C.

The region between the quarter circle and the corner B is shaded.

Show that the shaded area is more than 21% of the area of the square.

OABC6 cmDiagram NOT accurately drawn
4 marks
Show answer
Shaded area = 36 - 9pi = 7.725... cm2, which is 21.46...% of 36 cm2, and 21.46% > 21%.
7

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
8

A window is made from a rectangle with a semicircle on top.

The rectangle is 1.2 m high and 0.8 m wide. The semicircle sits exactly on top of the rectangle, so its diameter is 0.8 m.

Glass for the window costs £95 per square metre.

Work out the cost of the glass for the window. Give your answer correct to the nearest penny.

0.8 m1.2 mDiagram NOT accurately drawn
5 marks
Show answer
£115.08
9

A quarter circle has radius r cm.

The area of the quarter circle is 9π cm2.

  1. Work out the value of r.
  2. Work out the perimeter of the quarter circle. Give your answer correct to 1 decimal place.
4 marks
Show answer
a) 6 b) 21.4 cm
10

A square has sides of length 5 cm.

A circle is drawn through all four vertices of the square.

Calculate the circumference of the circle. Give your answer correct to 3 significant figures.

5 cmDiagram NOT accurately drawn
4 marks
Show answer
22.2 cm
11

OAB is a quarter circle with centre O. OA and OB are radii and angle AOB = 90°.

The straight line AB has length 10 cm.

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

10 cmOABDiagram NOT accurately drawn
4 marks
Show answer
12.5π cm²
12

A flower bed is a semicircle with diameter 20 m.

Fencing is to be put around the whole perimeter of the flower bed, including the straight side.

Fencing costs £4.20 per metre and is only sold in whole metres.

Work out the total cost of the fencing.

5 marks
Show answer
£218.40
13

The diagram shows a shape made from a square and a quarter circle.

The square OABC has sides of length 10 cm. The quarter circle has centre O and radius 10 cm, and is joined to the square along the side OC so that the two parts do not overlap.

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

OABC10 cm10 cmDiagram NOT accurately drawn
5 marks
Show answer
178.5 cm²
14

A square lawn has sides of length 8 m.

A flowerbed in the shape of a quarter circle of radius 8 m is dug in one corner of the lawn. The centre of the quarter circle is at the corner of the lawn.

The rest of the lawn is covered with turf. Turf costs £4.25 per square metre.

Work out the cost of the turf.

5 marks
Show answer
£58.37

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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