Mathematics, 14.10.2019 06:30 dsteele3642
The surface areas of two similar solids are 450mm squared and 578mm squared. if the volume of the smaller solid is 511mm cubed find the volume of the larger solid. round your answer to the nearest hundredth.
Answers: 3
![\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}}\\\\ -------------------------------\\\\](/tpl/images/0317/8166/70089.png)
![\bf \cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\implies \cfrac{\sqrt{450}}{\sqrt{578}}=\cfrac{\sqrt[3]{511}}{\sqrt[3]{v}}\implies \cfrac{15\sqrt{2}}{17\sqrt{2}}=\cfrac{\sqrt[3]{511}}{\sqrt[3]{v}} \\\\\\ \cfrac{15}{17}=\cfrac{\sqrt[3]{511}}{\sqrt[3]{v}}\implies \sqrt[3]{v}=\cfrac{17\sqrt[3]{511}}{15}\implies v=\left( \cfrac{17\sqrt[3]{511}}{15} \right)^3 \\\\\\ v=\cfrac{17^3\cdot 511}{15^3}](/tpl/images/0317/8166/9a35e.png)
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The surface areas of two similar solids are 450mm squared and 578mm squared. if the volume of the sm...
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