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

1.A circular garden pond has a diameter of 5 m. A gardener is laying gravel around it in a ring-shaped path 1 m wide, measured outward from the edge of the pond. Work out the area of the gravel path. Use π = 3.14.

2.A circular clock face has a radius of 9 cm. Work out the circumference of the clock face. Use π = 3.14. Give your answer to 1 decimal place.

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

4.A circular tabletop has a radius of 15 cm. Work out the area of the tabletop. Use π = 3.14. Give your answer to 1 decimal place.

5.All four sides of a rhombus are the same length. One side of a rhombus is 7 cm long. Work out the perimeter of the rhombus.

6.A party hat is in the shape of a cone with a base radius of 6 cm and a slant height of 10 cm. Work out the curved surface area of the party hat. Use π = 3.14 and the formula curved surface area = πrl.

7.A window is made from a rectangle with a semicircle on top. The rectangle is 40 cm wide and 60 cm tall. The semicircle has the same width as the rectangle. Work out the total area of the window. Use π = 3.14. Give your answer to the nearest whole number.

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

9.A rectangular name card has a perimeter of 30 cm. The card is 9 cm long. Work out the width of the card.

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

11.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.

12.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.

13.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.

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

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