Mathematics, 28.01.2020 12:31 simplemickey123
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question: an environmental provider sells hemispherical
an environmental provider sells hemispherical holding ponds for treatment of chemical waste. the volume of a pond is =1/2( 4/3pi x ^3), where is the radius in feet. the provider also sells cylindrical collecting tanks. a collecting tank fills completely and then drains completely to fill the empty pond. the volume of the tank is =12 pie x ^2, where is the radius of the tank.
given that the volumes are equal, =, write an equation that shows as a function of .
is it =?
Answers: 1
![\bf r_1^3=\cfrac{3}{2\pi x}\cdot 12\pi x r_2^2\implies r_1^3=\cfrac{3}{1}\cdot 6r_2^2 \\\\\\ r_1^3=18r_2^2\impliedby \textit{now, taking }\sqrt[3]{\qquad }\textit{ to both sides} \\\\\\ \sqrt[3]{r_1^3}=\sqrt[3]{18r_2^2}\implies r_1=\sqrt[3]{18r_2^2}](/tpl/images/0476/6797/f941b.png)
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