Mathematics, 25.11.2019 23:31 fowers7187
Adesign on the surface of a balloon is 9 cm wide when the balloon holds 62 cm3 of air. how much air does the balloon hold when the design is 18 cm wide?
Answers: 2
![\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{cccllll} &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{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\implies \cfrac{\sqrt{9}}{\sqrt{18}}=\cfrac{\sqrt[3]{62}}{\sqrt[3]{x}}](/tpl/images/0390/5206/8964d.png)
![\bf \\\\\\ \cfrac{3}{3\sqrt{2}}=\cfrac{\sqrt[3]{62}}{\sqrt[3]{x}}\implies \cfrac{1}{\sqrt{2}}=\cfrac{\sqrt[3]{62}}{\sqrt[3]{x}}\implies \sqrt[3]{x}=\sqrt{2}\cdot \sqrt[3]{62} \\\\\\ x=\left( \sqrt{2}\cdot \sqrt[3]{62} \right)^3\implies x=\sqrt{2^3}\cdot \sqrt[3]{62^3}\implies x=2\sqrt{2}\cdot 62 \\\\\\ \boxed{x=124\sqrt{2}}](/tpl/images/0390/5206/2ab31.png)
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Adesign on the surface of a balloon is 9 cm wide when the balloon holds 62 cm3 of air. how much air...
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