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kondaur [170]
3 years ago
8

A design 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?
Mathematics
1 answer:
Nimfa-mama [501]3 years ago
8 0
\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}}

\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}}
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