Mathematics, 29.06.2019 09:30 Happygirl5715
If two cylinders are similar in the ratio between the altitude lengths 2: 3 what is the ratio of their volumes
Answers: 1
![\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\[2em] \begin{array}{ccccllll} &\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\ \cline{2-4}&\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}\\\\[-0.35em] ~\dotfill](/tpl/images/0030/5477/a310b.png)
![\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}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\stackrel{\textit{ratio of the}}{sides}}{\cfrac{2}{3}}~\hspace{7em}\stackrel{\stackrel{\textit{ratio of the}}{volumes}}{\cfrac{2^3}{3^3}}\implies \cfrac{8}{27}\implies 8:27](/tpl/images/0030/5477/7a28f.png)
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