Two similar pyramids have lateral areas 20 ft2 and 45 ft2. The volume of the smaller pyramid is 8 ft3. What is the volume of the larger pyramid?

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13-06-2017
Mathematics

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Two similar pyramids have lateral areas 20 ft2 and 45 ft2. The volume of the smaller pyramid is 8 ft3. What is the volume of the larger pyramid?

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jdoe0001 jdoe0001 · Answer 1 · 2017-06-13T20:42:21+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} \\\\ -----------------------------\\\\ \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{small}{large}\qquad \cfrac{\sqrt{20}}{\sqrt{45}}=\cfrac{\sqrt[3]{8}}{\sqrt[3]{v}}\implies \cfrac{2\underline{\sqrt{5}}}{3\underline{\sqrt{5}}}=\cfrac{2}{\sqrt[3]{v}}\implies \cfrac{2}{3}=\cfrac{2}{\sqrt[3]{v}} \\\\\\ \sqrt[3]{v}=3\implies v=3^3\implies v=27[/tex]