Question

The pair of square pyramids are similar. Use the given information to find the scale factor of the smaller square pyramid to the larger square pyramid. V= 64 in, V= 343 in

Answer 1

$\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{ccccllll} &\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\ &-----&-----&-----\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}\\\\ -----------------------------$

$\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\ \stackrel{\stackrel{pyramids}{scale~factor}}{\cfrac{small}{large}}\qquad \qquad \cfrac{s}{s}=\cfrac{\sqrt[3]{64}}{\sqrt[3]{343}}\implies \cfrac{s}{s}=\cfrac{4}{7}\implies 4:7$