Circles, composite shapes, spheres, pyramids and cones worksheet — GCSE Foundation

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

2.A circular clock face has a diameter of 18 cm. Work out the circumference of the clock face. Use π = 3.14.

3.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.

4.A rectangular garden bed measures 5 m by 3 m. A semicircular flower border is attached along one of the 3 m-wide ends, on the outside of the rectangle, so that the 3 m side is the diameter of the semicircle. Work out the total perimeter of the combined shape (the two long sides, the one remaining short side, and the curved edge). Use π = 3.14.

5.A circle has a radius of 1 cm. Work out the circumference of the circle. Give your answer in terms of π.

6.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.

7.A solid pyramid has a square base of side 6 cm. Its apex is directly above the centre of the base, at a vertical height of 8 cm. Work out the volume of the pyramid.

8.A circular plate has a diameter of 20 cm. Work out the area of the plate. Use π = 3.14.

9.A circular coin has a diameter of 3 cm. Work out the circumference of the coin. Give your answer in terms of π.

10.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.

11.A triangular badge has two sides of length 8 cm and a third side of length 5 cm. Work out the perimeter of the badge.

12.An ice cream is made from a cone of radius 3 cm and height 10 cm, topped with a hemisphere of the same radius sitting exactly on top of the cone. Work out the total volume of the ice cream. Use π = 3.14. Give your answer to the nearest whole number. Volume of a cone = 1/3 × πr²h. Volume of a sphere = 4/3 × πr³.

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

14.A square tile has sides of length 4.5 cm. Work out the perimeter of the tile.

15.A solid pyramid has a square base of side 10 cm and four identical triangular faces. Its apex is directly above the centre of the base, at a vertical height of 12 cm, and the slant height of each triangular face — the distance from the apex to the midpoint of a base edge — is 13 cm. Work out the total surface area of the pyramid.