Geometry and measures worksheet — GCSE Higher

1.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.

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 circle has two straight radii drawn from the centre to the edge, together with the arc between them. Write down the name of the region enclosed by these two radii and the arc.

4.In triangle ABC, angle ABC = 47°, AC = 12.5 cm and BC = 9.2 cm. Work out the size of angle BAC. Give your answer to 1 decimal place.

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

6.A field ABCD is a convex quadrilateral. AB = 40 m, BC = 32 m and angle ABC = 95°. The other two sides are CD = 25 m and DA = 36 m. Work out the area of the field. Give your answer to the nearest square metre.

7.Two straight roads cross at a junction. The angle between them, measured with a protractor, is 118°. What is the size of the angle vertically opposite to it?

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 cuboid has length 3 cm, width 4 cm and height 12 cm. Work out the length of the diagonal that runs from one corner of the cuboid to the opposite corner.

10.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.

11.In triangle ABC, AB = 9 cm, BC = 6 cm and angle BAC = 35°. This description fits two different triangles. Work out the two possible sizes of angle ACB, each to 1 decimal place.

12.Two cylindrical storage tins are geometrically similar. The smaller tin has height 4 cm and the larger tin has height 6 cm. Work out the ratio of the surface area of the smaller tin to the surface area of the larger tin, giving your answer in the form a : b in its simplest form.

13.A right-angled triangle has a hypotenuse of 10 cm and one of its other angles is 45°. Work out the length of one of the two shorter sides. Give your answer to 1 decimal place.

14.A circle has a diameter of 24 cm. A sector of this circle has an angle of 90°. Using π = 3.14, work out the area of the sector.

15.The bearing of a harbour B from a ferry's position A is 260°. What is the bearing of A from B?