Question

The pair of square pyramids are similar. Use the given information to find the scale factorof the smaller square pyramid to the larger square pyramid.The scale factor is :)(Type whole numbers.)

Answer 1

If the scale factor of one figure to another one is k, then the ratio of their volumes is equal to:

$k^3$

The volume in cubic inches of the smaller pyramid is 27, while the volume of the bigger pyramid is 343. Then:

$k^3=\frac{27}{343}$

Take the cubic root to both members of the equation to isolate k:

$\begin{gathered} \Rightarrow k=\sqrt[3]{\frac{27}{343}} \\ =\frac{\sqrt[3]{27}}{\sqrt[3]{343}} \\ =\frac{3}{7} \end{gathered}$

Therefore, the scale factor of the smaller pyramid to the larger pyramid, is:

$\frac{3}{7}$