Geometry and measures worksheet — GCSE Foundation

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

2.A raised garden bed is a prism whose cross-section is a triangle with a base of 1.2 m and a perpendicular height of 0.8 m. The bed is 3 m long. Work out the volume of soil needed to fill it, in m³.

3.A plan of a school hall uses a scale of 1 : 250. A wall is drawn 3.4 cm long on the plan. Sam wants to know the wall's real length in metres. What is it?

4.A scale drawing uses a scale of 1 : 60. A path on the drawing is measured as 9.8 cm long. What is the real length of the path, in metres, to 1 decimal place?

5.A sector of a circle has radius 4 cm and angle 90°. Using π = 3.14, work out the area of the sector.

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 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.

8.Write down the exact value of sin 60°.

9.A sector of a circle has radius 10 cm and angle 72°. Using π = 3.14, work out the arc length of the sector.

10.A circular coaster has a radius of 4 cm. Work out the circumference of the coaster. Give your answer in terms of π.

11.A sector of a circle has radius 9 cm and angle 40°. Work out the area of the sector, in terms of π.

12.A circular tabletop has a radius of 15 cm. Work out the area of the tabletop. Use π = 3.14. Give your answer to 1 decimal place.

13.A running track has a straight section and a semicircular bend. The bend is a semicircle with radius 32 m. Work out the length of the curved part of the bend, to 1 decimal place. (Use π = 3.14.)

14.A circular coin has a diameter of 3 cm. Work out the circumference of the coin. Give your answer in terms of π.

15.A trapezium has parallel sides of length 6 cm and 10 cm, and a perpendicular height of 4 cm. Work out its area.