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

1.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.

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

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

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

6.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.

7.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.

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

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

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

11.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.

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 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.

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

15.A cylindrical candle and a cone-shaped candle have the same base radius and the same height. State the cone's volume as a fraction of the cylinder's volume.