If the ratio of the sides of two similar prisms is 3:5 and the volume of the first prism is 54, what is the volume of the second prism?

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21-07-2017
Mathematics

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If the ratio of the sides of two similar prisms is 3:5 and the volume of the first prism is 54, what is the volume of the second prism?

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jdoe0001 jdoe0001 · Answer 1 · 2017-07-21T01:01:31+02:00

[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} \\\\ -----------------------------\\\\[/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}}\\\\ -------------------------------\\\\ \cfrac{smaller}{larger}\qquad \cfrac{s^3}{s^3}=\cfrac{\textit{volume of smaller}}{\textit{volume of larger}}\implies \cfrac{3^3}{5^3}=\cfrac{54}{v} \\\\\\ v=\cfrac{5^3\cdot 54}{3^3}[/tex]