Using relevant formulae the volume and surface area of cuboids, cubes, prisms, cylinders, spheres, cones and composite shapes can be calculated.

Before doing this section you should revise the National 4 Lifeskills Maths section on Volume.

Often volume questions at National 5 involve a **composite solid** (a solid made up of at least two basic solids).

It is possible to calculate the volume of composite solids by simply splitting the composite solid into smaller solids and finding their separate volumes. The volumes of each of the individual solids are then added together to give the volume of the composite solid.

Remember that the volume of each simple solid can be found using simple a formula.

- \[Volume~of~cuboid = length \times breadth \times height\]
- \[Volume~of~cube = length^3 = length \times length \times length\]
- \[Volume~of~prism= area\,of\,cross-section\,\times height\]
- \[Volume~of~sphere = \frac{4}{3}\pi r^3\]
- \[Volume~of~pyramid = \frac{1}{3}base\,height\]
- \[Volume~of~cone = \frac{1}{3}\pi r^2h\]