Geometry and measures worksheet — GCSE Foundation

1.Two straight lines PQ and RS cross at point O. Angle POR = 52°. Work out angle QOS.

2.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.

3.A model car is built to a scale of 1 : 24. The real car is 4.32 m long. Work out the length of the model, in centimetres.

4.A student draws a net using 5 identical squares arranged in a row of four with one extra square attached to the side of one of them. Can this net be folded to make a closed cube?

5.A church tower is due east of a village. What is the three-figure bearing of the church tower from the village?

6.A vertical flagpole casts a shadow 6 m long at the same time as a 1.2 m vertical post casts a shadow 1.8 m long. The flagpole and the post are both vertical, and the triangles formed by each object, its shadow, and the sun's ray are similar. Work out the height of the flagpole.

7.A solid cone has a base radius of 6 cm and a vertical height of 10 cm. Work out the volume of the cone. Use π = 3.14 and give your answer correct to 1 decimal place.

8.A zip wire is fixed at an angle of 50° to the horizontal, running from a high platform down to the ground. The zip wire itself, from the platform to the ground, is 12 m long. Work out the horizontal distance covered by the zip wire. Give your answer correct to 1 decimal place.

9.A composite solid is made from a cylinder of radius 3 cm and height 10 cm, with a cone of the same radius and vertical height 4 cm fixed on top, apex upward. Work out the total volume of the solid. Use π = 3.14 and give your answer correct to 1 decimal place.

10.A sector of a circle has radius 7 cm and angle 90°. Using π = 3.14, work out the arc length of the sector, to 1 decimal place.

11.A cyclist rides around a perfectly circular track with centre O. At every moment of the ride, the distance from O to the cyclist is exactly the same. Which term names this fixed distance?

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

13.Write down the term for the distance all the way around the edge of a circle.

14.A cuboid-shaped shipping crate has a length of 12 m, a width of 5 m, and a volume of 360 m³. Work out the height of the crate, in metres.

15.A sector of a circle has radius 6 cm and an arc length of 15.7 cm. Using π = 3.14, work out the angle of the sector.