It is important to note the units

of length:

of length:

of volume:

We can relate these directly to the scale factors between the lengths, areas and volumes of similarly objects – that is, mathematically similar, with only a scale factor to separate them. As shown on the diagram below, if the scale factor for lengths isthen the scale factor for areas isand the scale factor for volumes is

All the length of the sides of the solid on the right are twice the lengths of corresponding sides on the left.

If the area of the cuboid on the left isand the volume is

the area of the cuboid on the right is

the volume of the cuboid on the right is

All the length of the sides of the solid on the right are three times the lengths of corresponding sides on the left.

If the area of the cuboid on the right isand the volume is

the area of the cuboid on the left is

the volume of the cuboid on the left is