19.6 Composite shapes and solids — Practise

1. An L-shape is made by removing a 3 cm by 2 cm rectangle from a 9 cm by 6 cm rectangle. Work out its area.
2. A rectangle 10 cm by 8 cm has a 4 cm by 3 cm rectangle removed. Work out the remaining area.
3. A shape is made from a rectangle 7 cm by 4 cm and a triangle with base 7 cm and height 3 cm. Work out its area.
4. A semicircle of radius 4 cm is joined to a rectangle 8 cm by 5 cm along the rectangle length. Work out the outer perimeter in terms of π.
5. A solid is made from a cuboid 5 cm by 4 cm by 3 cm and a cuboid 2 cm by 4 cm by 3 cm joined along a 4 cm by 3 cm face. Work out its volume.
6. Two cuboids of dimensions 4 cm by 3 cm by 2 cm and 5 cm by 3 cm by 2 cm are joined along a 3 cm by 2 cm face. Work out the outside surface area.
7. A solid consists of a cylinder of radius 3 cm and height 4 cm with a hemisphere of radius 3 cm on top. Work out its volume in terms of π.
8. A shape has area 72 cm². A square of side 4 cm is cut from it. Work out the remaining area and explain why you subtract.
9. A solid is a cuboid 10 cm by 4 cm by 2 cm with a cylindrical hole of radius 2 cm drilled through its 2 cm height. Which method finds the remaining volume: add the volumes, or subtract the hole from the cuboid? Give a reason, then work it out in terms of π.