Respuesta :
[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{\textit{small cylinder}}{\textit{large cylinder}}\qquad \cfrac{r}{4r}=\cfrac{h}{4h}=\cfrac{1}{4}\impliedby ratio \\\\\\ now\qquad \cfrac{1^3}{4^3}=\cfrac{\textit{smaller volume}}{\textit{larger volume}}\implies \cfrac{1}{64}=\cfrac{10}{v}\implies v=64\cdot 10[/tex]
[tex]\bf \cfrac{\textit{small cylinder}}{\textit{large cylinder}}\qquad \cfrac{r}{4r}=\cfrac{h}{4h}=\cfrac{1}{4}\impliedby ratio \\\\\\ now\qquad \cfrac{1^3}{4^3}=\cfrac{\textit{smaller volume}}{\textit{larger volume}}\implies \cfrac{1}{64}=\cfrac{10}{v}\implies v=64\cdot 10[/tex]
