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.
A circle has radius 6 cm.
A circle has diameter 18 cm.
The circumference of a circle is 14π cm.
Work out the area of the circle. Give your answer in terms of π.
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.
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.
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.
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.
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.
A quarter circle has radius r cm.
The area of the quarter circle is 9π cm2.
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.
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.
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.
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.
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.
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.