Geometry and measures worksheet — GCSE Foundation

1.The top of a clock tower is 25 m above level ground. Oliver stands on the ground 25 m from the foot of the tower. Work out the angle of elevation of the top of the tower from the point where Oliver stands.

2.A fan-shaped rug is in the shape of a sector of a circle with radius 4 m and angle 180°. It costs £4 per square metre to make. Using π = 3.14, work out the total cost of the rug.

3.A fish tank is a cuboid measuring 40 cm long, 25 cm wide and 30 cm high. Water is poured in to a depth of 20 cm. Work out the volume of water in the tank, in litres.

4.A shop stacks identical storage crates in a display. The diagram shows the plan of the floor positions used, with one corner position marked. Every floor position is filled with crates stacked 3 high, except the marked corner position, which is left completely empty. Work out how many crates are used in total.

5.A sector of a circle has radius 15 cm and angle 216°. Using π = 3.14, work out the arc length of the sector.

6.A triangular prism has a cross-section that is a triangle with a base of 3.5 cm and a perpendicular height of 4 cm. The prism is 10 cm long. Work out the volume of the prism.

7.A sector of a circle has radius 12 cm and angle 45°. Using π = 3.14, work out the area of the sector.

8.A footpath sign shows a distance of 0.45 km to the next village. Work out this distance in metres.

9.A footpath is 3750 m long. Work out this distance in kilometres.

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

11.A sector of a circle has radius 6 cm and angle 60°. Work out the arc length of the sector, in terms of π.

12.The curved part of a circle's circumference, between two points on the circle, has its own name. Write down this name.

13.A ship sails 12 km on a bearing of 070° from a harbour to a buoy. It then sails a further 9 km, still on a bearing of 070°, from the buoy to a lighthouse. How far is the lighthouse from the harbour, in kilometres?

14.A circular garden pond has a diameter of 5 m. A gardener is laying gravel around it in a ring-shaped path 1 m wide, measured outward from the edge of the pond. Work out the area of the gravel path. Use π = 3.14.

15.A photocopier enlarges a document so that every length is multiplied by the same scale factor. A line on the original document is 3.2 cm long, and the same line measures 11.2 cm on the enlarged copy. A second line on the original document is 2.5 cm long. Work out the length of the second line on the enlarged copy, giving your answer to 2 decimal places.