[tex]\bf \qquad \qquad \textit{ratio relations}
\\\\
\begin{array}{ccccllll}
&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{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\
-------------------------------\\\\[/tex]
[tex]\bf \cfrac{small}{large}\qquad \cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\qquad thus\qquad \cfrac{\sqrt[3]{27}}{\sqrt[3]{1331}}=\cfrac{\sqrt{18}}{\sqrt{a}}
\\\\\\
\cfrac{3}{11}=\sqrt{\cfrac{18}{a}}\implies \left( \cfrac{3}{11} \right)^2=\cfrac{18}{a}\implies \cfrac{3^2}{11^2}=\cfrac{18}{a}\implies a=\cfrac{11^2\cdot 18}{3^2}[/tex]
and surely, you know how much that is.
