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

1.A shape is made by joining two rectangles edge to edge, with no overlap. One rectangle measures 12 cm by 4 cm and the other measures 4 cm by 8 cm. Work out the total area of the shape.

2.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.

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

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

5.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.

6.A composite solid is made from a cylinder of radius 3 cm and height 10 cm, with a cone of the same radius and vertical height 4 cm fixed on top, apex upward. Work out the total volume of the solid. Use π = 3.14 and give your answer correct to 1 decimal place.

7.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.

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

9.A cylindrical water tank has a solid hemispherical dome on top, both with radius 2 m. Work out the volume of the hemispherical dome alone. Use π = 3.14 and give your answer correct to 3 decimal places.

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

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

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

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

14.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.

15.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.