## 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 prisms can be calculated using formulae.

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

### 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.

 into cm3. From the diagram 1 m3 = 100 × 100 × 100cm3 = 1 000 000 cm3

### Volume and surface area formulae of Prisms

All of the shapes below are called prisms.

prism is an object with a regular cross section (shaded in the diagrams below).

Volume of a prism = area of cross section × length

(This formula is sometimes given as Volume of prism = area of base × height)

.

 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 Triangular Prism V = ( shaded area ) × l    = ( 1⁄2 × b × h ) × l S = bl + al + cl + bh Cylinder V = ( shaded area ) × h    = ( πr2 ) × h    = πr2h S = 2πr2 + 2πrh    = 2πr( r + h )

### Volume of Other Solids.

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

If the solid is an irregular shape, other methods such as finding how much water it displaces when put into water have to be used!

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