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 is
then the scale factor for areas is
and 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 is
and 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 is
and the volume is
the area of the cuboid on the left is
the volume of the cuboid on the left is