a dimension of a sphere is its radius, so it correlates with its volume, thus
[tex]\bf \qquad \qquad \textit{ratio relations}
\\\\
\begin{array}{ccccllll}
&\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\
&-----&-----&-----\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3}
\end{array}\\\\
-----------------------------[/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}}\\\\
-------------------------------\\\\
%The volume of two spheres are 327\pi in^{3} and 8829\pi in^{3}
\cfrac{small}{large}\qquad \cfrac{s}{s}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\implies \cfrac{s}{s}=\cfrac{\sqrt[3]{327}}{\sqrt[3]{8829}}\qquad
\begin{cases}
8829=3\cdot 3\cdot 3\cdot 327\\
\qquad 3^3\cdot 327
\end{cases}[/tex]
[tex]\bf \cfrac{s}{s}=\cfrac{\sqrt[3]{327}}{\sqrt[3]{3^3\cdot 327}}\implies \cfrac{s}{s}=\cfrac{\underline{\sqrt[3]{327}}}{3\underline{\sqrt[3]{327}}}\implies \cfrac{s}{s}=\cfrac{1}{3}[/tex]
