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

3.A solid metal sphere has a radius of 5 cm. It is melted down and recast into a solid cylinder with the same radius, 5 cm. Work out the height of the cylinder, so that its volume equals the volume of the sphere. Use π = 3.14 and give your answer correct to 1 decimal place.

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

5.A right-angled triangle has a hypotenuse of 10 cm. One of its other angles is 45°. Work out the exact length of one of the two shorter sides.

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

7.Two similar signs have lengths in the ratio 9 : 4. The larger sign has a side of length 14.4 cm. Work out the length of the corresponding side of the smaller sign.

8.A triangular sail for a small boat has a base of 2.4 m and a height of 1.75 m. Sailcloth costs £12.50 per m². Work out the total cost of the sailcloth needed for the sail.

9.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.

10.A fan-shaped rug is in the shape of a sector of a circle with radius 4 m and angle 180°. It costs £4 per square metre to make. Using π = 3.14, work out the total cost of the rug.

11.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.

12.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.

13.A cylinder has a radius of 5 cm. Its volume is 471 cm³. Using π = 3.14, work out the height of the cylinder.

14.A line segment is measured with a ruler and found to be 6.5 cm long. What is this length in millimetres?

15.A plan of a school hall uses a scale of 1 : 250. A wall is drawn 3.4 cm long on the plan. Sam wants to know the wall's real length in metres. What is it?