Mathematics, 20.11.2019 07:31 fjdkj
The scale factor of a model of a hot air balloon to the actual hot air balloon is 1 to 5. the volume of the actual balloon is 5000 m^3 what is the volume ? a. 0.005 m^3 b.0.025 m^3 c. 40 m^3 d.200 m^3
Answers: 1
![\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/0382/7042/e3ab0.png)
![\bf \cfrac{model}{actual}\qquad \cfrac{s}{s}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\implies \cfrac{1}{5}=\cfrac{\sqrt[3]{v}}{\sqrt[3]{5000}}\implies \cfrac{1}{5}=\sqrt[3]{\cfrac{v}{5000}} \\\\\\ \left( \cfrac{1}{5} \right)^3=\cfrac{v}{5000}\implies \cfrac{1^3}{5^3}=\cfrac{v}{5000}\implies \cfrac{1}{125}=\cfrac{v}{5000} ](/tpl/images/0382/7042/753af.png)
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The scale factor of a model of a hot air balloon to the actual hot air balloon is 1 to 5. the volume...
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