MATH SOLVE

2 months ago

Q:
# what is the surface area of the smaller cone

Accepted Solution

A:

[tex]\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\\\ \begin{array}{ccccllll} &\stackrel{\stackrel{ratio}{of~the}}{Sides}&\stackrel{\stackrel{ratio}{of~the}}{Areas}&\stackrel{\stackrel{ratio}{of~the}}{Volumes}\\ \cline{2-4}&\\ \cfrac{\stackrel{similar}{shape}}{\stackrel{similar}{shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}~\hspace{6em} \cfrac{s}{s}=\cfrac{\sqrt{Area}}{\sqrt{Area}}=\cfrac{\sqrt[3]{Volume}}{\sqrt[3]{Volume}} \\\\[-0.35em] ~\dotfill[/tex][tex]\bf \cfrac{small~cone}{large~cone}\qquad \stackrel{\textit{sides ratio}}{\cfrac{2}{3}}=\stackrel{\textit{areas ratio}}{\cfrac{\sqrt{x}}{\sqrt{75}}}\implies \cfrac{2}{3}=\sqrt{\cfrac{x}{75}}\implies \left( \cfrac{2}{3} \right)^2=\cfrac{x}{75} \\\\\\ \cfrac{4}{9}=\cfrac{x}{75}\implies 300=9x\implies \cfrac{300}{9}=x\implies \cfrac{100}{3}=x[/tex]