find the similarity ratio of a cube with volume 216 ft to a cube with volume 1000ft

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tsutton tsutton

25-05-2017
Mathematics

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find the similarity ratio of a cube with volume 216 ft to a cube with volume 1000ft

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jdoe0001 jdoe0001 · Answer 1 · 2017-05-25T02:19:11+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{s^3}{s^3}\implies \cfrac{216}{1000}\implies \cfrac{\sqrt[3]{216}}{\sqrt[3]{1000}}\implies \cfrac{s}{s}\impliedby \textit{similarity ratio}[/tex]

and simplify it away