[tex]\bf \qquad \qquad \textit{ratio relations}
\\\\
\begin{array}{cccllll}
&Sides&Area&Volume\\
&-----&-----&-----\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3}
\end{array}\\\\
-----------------------------\\\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\implies \cfrac{\sqrt{9}}{\sqrt{18}}=\cfrac{\sqrt[3]{62}}{\sqrt[3]{x}}[/tex]
[tex]\bf \\\\\\
\cfrac{3}{3\sqrt{2}}=\cfrac{\sqrt[3]{62}}{\sqrt[3]{x}}\implies \cfrac{1}{\sqrt{2}}=\cfrac{\sqrt[3]{62}}{\sqrt[3]{x}}\implies \sqrt[3]{x}=\sqrt{2}\cdot \sqrt[3]{62}
\\\\\\
x=\left( \sqrt{2}\cdot \sqrt[3]{62} \right)^3\implies x=\sqrt{2^3}\cdot \sqrt[3]{62^3}\implies x=2\sqrt{2}\cdot 62
\\\\\\
\boxed{x=124\sqrt{2}}[/tex]
