[tex] \bf ~\hspace{5em} \textit{ratio relations of two similar shapes}
\\[2em]
\begin{array}{ccccllll}
&\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\
\cline{2-4}&\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3}
\end{array}\\\\[-0.35em]
~\dotfill [/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}}\\\\[-0.35em]
\rule{34em}{0.25pt}\\\\
\cfrac{s}{s}=\cfrac{1}{3}~\hspace{7em}\cfrac{1}{3}=\cfrac{\sqrt[3]{x}}{\sqrt[3]{2106}}\implies \cfrac{1}{3}=\sqrt[3]{\cfrac{x}{2106}}\implies \left( \cfrac{1}{3} \right)^3=\cfrac{x}{2106}
\\\\\\
\cfrac{1}{27}=\cfrac{x}{2106}\implies \cfrac{2106}{27}=x\implies 78=x [/tex]
