Geometry and measures worksheet — GCSE Foundation

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

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

3.A plumber charges a £45 call-out fee, plus £28 for each hour worked. She works on a job for 3 hours 30 minutes, and her hours are billed by rounding up to the next whole hour. Work out the total amount she charges.

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

5.A ship's radar can detect other ships up to 20 km away, over a sector-shaped area with angle 90°. A monitoring company charges £0.50 per square kilometre covered by one radar sweep. Using π = 3.14, work out the total charge for one sweep.

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

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.A sector of a circle has an angle of 90° and an area of 78.5 cm². Using π = 3.14, work out the radius of the circle.

9.A survey team measures the angle between two fences with a protractor and gets a reading of 254°. What type of angle is this?

10.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.

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

12.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.

13.A recipe uses 1.25 kg of flour. Work out how many grams of flour this is.

14.A market stall sells apples at £2.40 per kilogram. Which of these expressions gives the cost, in pounds, of buying m kilograms of apples?

15.A trapezium-shaped garden bed has parallel sides of 2.5 m and 4.5 m, and a perpendicular width of 3 m. A gardener wants to know the area of the bed before ordering topsoil. Work out the area of the garden bed.