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

1.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.

2.A rectangular photograph is 12 cm long and 5 cm wide. Work out the perimeter of the photograph.

3.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.

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

5.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.

6.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.

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

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

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

11.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.

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.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.

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

15.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.