Q:

What is the similarity ratio of a prism with surface area 36 ft2 to a similar prism with surface area 225 ft2?

Accepted Solution

A:
[tex]\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} \\\\-----------------------------\\\\[/tex][tex]\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}}\\\\ -------------------------------[/tex][tex]\bf \stackrel{sides}{\cfrac{s^2}{s^2}}=\stackrel{areas}{\cfrac{36}{225}}\implies \left( \cfrac{s}{s} \right)^2=\cfrac{36}{225}\implies \cfrac{s}{s}=\sqrt{\cfrac{36}{225}} \implies \cfrac{s}{s}=\cfrac{\sqrt{36}}{\sqrt{225}} \\\\\\ \cfrac{s}{s}=\cfrac{6}{15}\implies \cfrac{s}{s}=\cfrac{2}{5}\qquad \qquad \stackrel{\textit{similarity ratio}}{s~:~s\implies 2~:~5}[/tex]