Geometry and measures worksheet — GCSE Foundation

1.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.

2.A circular pizza base has a radius of 12 cm. Work out the area of the pizza base. Use π = 3.14.

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

4.A parallelogram has a base of 9 cm and a perpendicular height of 4 cm. Work out its area.

5.In triangle ABC the angle at C is 90°, AC = 8 cm and the angle at A is 30°. Work out the length of BC. Give your answer to 1 decimal place.

6.A solid cone has a base radius of 6 cm and a vertical height of 10 cm. Work out the volume of the cone. Use π = 3.14 and give your answer correct to 1 decimal place.

7.A vertical line passes through the point (5, 2). Write down the equation of this line.

8.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.

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

10.Lines PQ and RS are parallel. A straight line crosses PQ at point X and crosses RS at point Y. Angle PXY = 63°. Angle PXY and angle XYS are co-interior (allied) angles, which add up to 180°. Work out the size of angle XYS.

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

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

13.A student draws a net using 5 identical squares arranged in a row of four with one extra square attached to the side of one of them. Can this net be folded to make a closed cube?

14.A warehouse stores identical cube-shaped crates. Its plan view is a 2 by 4 rectangle of crate positions, and every position is filled to a height of 3 crates, except one corner position, which has only 2 crates stacked on it because a delivery was incomplete. How many crates are there in total?

15.A square has sides of length 7 cm. Work out its area.