Geometry and measures worksheet — GCSE Foundation

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

2.A sector of a circle has radius 15 cm and angle 216°. Using π = 3.14, work out the arc length of the sector.

3.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?

4.A cylinder has a radius of 3 cm and a height of 10 cm. Using π = 3.14, work out the volume of the cylinder.

5.A birthday cake is a cylinder of radius 10 cm and height 8 cm, with a thin ribbon fixed exactly once around the curved side, at half the height, and joined with no overlap. Work out the length of ribbon needed. Use π = 3.14.

6.A trapezium has parallel sides of 5.6 cm and 8.4 cm, and a perpendicular height of 4 cm. Work out the area of the trapezium.

7.Two vertical masts stand on level ground, 40 m apart. One mast is 30 m tall and the other is 50 m tall. Work out the straight-line distance between the tops of the two masts. Give your answer to 1 decimal place.

8.A parallelogram has an area of 84 cm² and a base of 12 cm. Work out the perpendicular height of the parallelogram.

9.A quadrilateral has both pairs of opposite sides parallel and equal in length, but none of its angles are right angles. Which statement about this quadrilateral is correct?

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

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

12.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?

13.A cuboid has three different edge lengths: a length, a width and a height, all different from each other. How many rectangles make up its net in total?

14.A quadrilateral has angles of 100°, 85° and 95° at three of its vertices. Work out the fourth angle.

15.A circular decoration has a radius of 10 cm. A ribbon costs £0.50 per centimetre and is fixed along the curved edge (the arc) of a sector-shaped section with an angle of 90°. Using π = 3.14, work out the cost of the ribbon for this section.