Geometry and measures worksheet — GCSE Foundation

1.A model of a bridge is built to a scale where every length on the model is 1/240 of the matching length on the real bridge. A support beam on the model measures 3.6 cm. Work out the length of the real support beam, giving your answer in metres.

2.A circle has diameter 10 cm. Using π = 3.14, work out the circumference of the circle.

3.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.

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

5.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.

6.a is the column vector with top number 3 and bottom number −2. Work out 4a, giving your answer as a column vector in the form (top, bottom).

7.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?

8.A drone flies from its base in three stages, each stage measured in metres east and north as a column vector. Stage 1 is the column vector with top number 30 and bottom number 40. Stage 2 is the column vector with top number −10 and bottom number 20. Stage 3 is the column vector with top number 15 and bottom number −5. Work out the column vector that would take the drone in a single straight flight back to its base from where it ends up.

9.Three angles meet at a single point on one side of a straight line. Two of the angles are 48° and 65°. Work out the third angle.

10.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.

11.The diagram shows a cuboid. Work out the area of its front elevation, in square centimetres.

12.A map has a scale of 1 : 20 000. The distance between two villages is 3.4 km in real life. How long is this distance on the map, in centimetres?

13.Write down the name given to a triangle whose three sides are all the same length.

14.A garden flower bed is in the shape of a trapezium. Its two parallel edges are 3.5 m and 6.5 m long, and the perpendicular distance between them is 4 m. Bedding plants cost £2.50 per square metre to cover the bed. Work out the total cost of the bedding plants.

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