Mathematics, 12.07.2019 20:30, jferdi2005
The cylinders are similar. the volume of the larger cylinder is 2106 cubic centimeters. what is the volume of the smaller cylinder?
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/0082/2339/692a5.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}\\\\ \cfrac{s}{s}=\cfrac{1}{3}~\hspace{7em}\cfrac{1}{3}=\cfrac{\sqrt[3]{x}}{\sqrt[3]{2106}}\implies \cfrac{1}{3}=\sqrt[3]{\cfrac{x}{2106}}\implies \left( \cfrac{1}{3} \right)^3=\cfrac{x}{2106} \\\\\\ \cfrac{1}{27}=\cfrac{x}{2106}\implies \cfrac{2106}{27}=x\implies 78=x](/tpl/images/0082/2339/353c0.png)
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