[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{smaller}{larger}\qquad \cfrac{s}{s}=\cfrac{\sqrt[3]{s}}{\sqrt[3]{s}}\implies \cfrac{s}{s}=\cfrac{\sqrt[3]{250}}{\sqrt[3]{1024}}\implies \cfrac{s}{s}=\cfrac{\sqrt[3]{2\cdot 5^3}}{\sqrt[3]{2^9\cdot 2}}
\\\\\\
\cfrac{s}{s}=\cfrac{5\sqrt[3]{2}}{\sqrt[3]{(2^3)^3\cdot 2}}\implies \cfrac{s}{s}=\cfrac{5\sqrt[3]{2}}{8\sqrt[3]{2}}\implies \cfrac{s}{s}=\cfrac{5}{8}[/tex]
