Concept

Length, Area, and Volume Scale Factors

When calculating the ratio between a measurement of two given objects, the lengths of their corresponding sides can be used. To calculate the length scale factor, the length $a$ of a side in the first figure is divided by the length $b$ of the corresponding side in the second figure. This ratio can then be squared to obtain the area scale factor or cubed to find the volume scale factor.

Type of Measurement	Ratio	Example
Length	$\frac{a}{b}$	$\frac{1}{2}$
Area	$(\frac{a}{b})^{2} = \frac{a ^{2}}{b ^{2}}$	$\frac{1 ^{2}}{2 ^{2}} = \frac{1}{4}$
Volume	$(\frac{a}{b})^{3} = \frac{a ^{3}}{b ^{3}}$	$\frac{1 ^{3}}{2 ^{3}} = \frac{1}{8}$