## Volume and Surface Area

The volume of an object is the measure of the amount of space it takes up.

The volumes and surface areas of certain simple objects such as cubes and cuboids can be calculated using formulae.

The surface area of an object is the total area of the outside surfaces of the object.

Finding Volumes − by counting cubes

For the cuboid or rectangular prism like the one shown it is possible to count cubes to find the volume of the object.

 Assuming that the cuboid is solid, there would be 16 cubes. If each cube has a side of 1 cm, we say its volume is 16 cubic centimetres or 16 cm3.

### Finding Volumes − by using a formula

It can be seen in the cuboid above that there are four rows of two cubes on the bottom level and there are two levels so a quicker way to find the volume would be to multiply 2 by 4 by 2. This method gives an equation or formula, which works for any cuboid or rectangular prism:

Volume = length × width × height = 4 × 2 × 2 = 16 cubic centimetres.

### Units

The units used for measuring volumes depends on the units used for measuring the lengths of the sides of the object.

A cubic metre is the area occupied by a cube with each side 1 metre long. It is written as 1 m3.

Common units for volume are:

 Unit Symbol Units for measuring: cubic centimetres cm3 Small objects such as a shoe box cubic metres m3 Size of a shipping container cubic kilometres km3 Amount of ash thrown out in a large volcanic eruption

A commonly used unit for measuring the volume or capacity of liquids is the litre.

1 litre is equivalent to the volume of a cube of side 10 cm.

1 litre = 10 cm × 10 cm × 10 cm = 1000 cm3

### Converting between units

To convert between units of volume is sometimes confusing. A diagram often helps.

e.g.

 Cubic metres into cubic centimetres From the diagram: 1 m3 = 100 × 100 × 100 cm3 = 1 000 000 cm3

### Volume and Surface Area of Cubes and Cuboids

The surface area of a solid shape is the total area of all of its faces. These are quite easy to work out for cubes and cuboids.

 Solid Name Volume Surface Area(sum of areas of all faces) Cube V = l × l × l = l3 S = 2l2+ 2l2+ 2l2 = 6l2 Cuboid or Rectangular Prism V = (shaded area) × l = (b × h) × l = bhl S = 2bh + 2hl + 2bl = 2(bh + hl + bl)

### Volume of Other Solids.

The volumes of composite solids can be found by breaking the solid up into smaller solids such as cubes and cuboids.

If the solid is an irregular shape, other methods for finding volumes have to be used.

Try this useful activity on the volume and surface area of cuboids and triangular prisms