[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{4}{8}\implies \cfrac{s}{s}=\cfrac{1}{2}~\hspace{7em}\cfrac{1}{2}=\cfrac{\sqrt[3]{x}}{\sqrt[3]{2264}}\implies \cfrac{1}{2}=\sqrt[3]{\cfrac{x}{2264}}
\\\\\\
\left( \cfrac{1}{2} \right)^3=\cfrac{x}{2264}\implies \cfrac{1}{8}=\cfrac{x}{2264}\implies \cfrac{2264}{8}=x\implies 283=x [/tex]
