Mathematics, 19.11.2019 21:31 ammarsico19
The volumes of two similar solids are 210 m3 and 1,680 m3. the surface area of the larger solid is 856 m2. what is the surface area of the smaller solid?
Answers: 3
![scale \ factor=\sqrt[3]{8} \\ scale \ factor= 2](/tpl/images/0381/8508/d3b22.png)
![\bf \textit{ratio relations}\\ \begin{array}{llll} sides&\cfrac{s}{s}\\\\ Area&\cfrac{s^2}{s^2}\\\\ Volume&\cfrac{s^3}{s^3} \end{array}\qquad thus\\\\ -----------------------------\\\\ \cfrac{\textit{smaller volume}}{\textit{bigger volume}}\implies \cfrac{210}{1680}=\cfrac{s^3}{s^3}\implies \cfrac{210}{1680}=\left( \cfrac{s}{s} \right)^3 \\\\\\ \sqrt[3]{\cfrac{210}{1680}}=\cfrac{s}{s}\implies \cfrac{\sqrt[3]{210}}{\sqrt[3]{1680}}=\cfrac{s}{s}\\\\ -----------------------------\\\\ ](/tpl/images/0381/8508/aa8b6.png)
![\bf now \\\\ \cfrac{\textit{smaller area}}{\textit{bigger area}}\implies \cfrac{A}{856}=\cfrac{s^2}{s^2}\implies \cfrac{A}{856}=\left( \cfrac{s}{s}\right)^2 \\\\\\\\ \textit{however, recall that }\sqrt[3]{\cfrac{210}{1680}}=\cfrac{s}{s}\qquad thus \\\\\\\\ \cfrac{A}{856}=\left( \sqrt[3]{\cfrac{210}{1680}}\right)^2\implies \cfrac{A}{856}=\cfrac{\sqrt[3]{210^2}}{\sqrt[3]{1680^2}}](/tpl/images/0381/8508/858d6.png)
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The volumes of two similar solids are 210 m3 and 1,680 m3. the surface area of the larger solid is 8...
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