Question

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

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} \\\\

-----------------------------$

$\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------$

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

Answer 2

Answer: 6:15___{2:5}

The reduce it by dividing by 3.

6/3 =2.

15/3 =5.

= {2:5}