Geometry and measures worksheet — GCSE Foundation

1.A sector of a circle has radius 6 cm and an area of 4.71 cm². Using π = 3.14, work out the angle of the sector.

2.A cake recipe takes 135 minutes from start to finish. Write this time as hours and minutes.

3.A quadrilateral has angles of 100°, 85° and 95° at three of its vertices. Work out the fourth angle.

4.A water tank is a cube with edges of length 2 m. Work out how many cubic centimetres the tank holds when it is full.

5.A sector of a circle has radius 9 cm and angle 120°. Using π = 3.14, work out the arc length of the sector, to 1 decimal place.

6.A solid rubber ball has a radius of 3 cm. Work out the volume of the ball. Use π = 3.14.

7.A hiker walks on a bearing of 065°. She then turns clockwise through 90° and continues walking in a straight line. What bearing is she now walking on?

8.A flagpole is 12 m tall. Freya stands 9 m from the base of the flagpole on level ground. Work out the angle of elevation of the top of the flagpole from where Freya stands. Give your answer correct to 1 decimal place.

9.A solid ball has a radius of 7 cm. Work out the surface area of the ball. Use π = 3.14.

10.A goat is tied by a rope 7 m long to a post at a corner of a rectangular field, where two fences meet at a right angle. The goat can reach anywhere inside the field that the rope allows. Using π = 3.14, work out the area the goat can graze, to the nearest square metre.

11.A parallelogram has an area of 84 cm² and a base of 12 cm. Work out the perpendicular height of the parallelogram.

12.A tap fills a tank at a rate of 18 litres per minute. The tank holds 0.45 m³. Work out how long the tap takes to fill the tank.

13.A trapezium has parallel sides of 5.6 cm and 8.4 cm, and a perpendicular height of 4 cm. Work out the area of the trapezium.

14.A line segment is measured with a ruler and found to be 6.5 cm long. What is this length in millimetres?

15.Two straight roads cross at a junction. The angle between them, measured with a protractor, is 118°. What is the size of the angle vertically opposite to it?