Mathematics, 21.10.2019 22:00 jason9394
Gas is escaping from a spherical balloon at the rate of 12 ft3/hr. at what rate (in feet per hour) is the radius of the balloon changing when the volume is 300 ft3?
Answers: 1
be the radius and 
the volume.
because the volume is decreasing, and we want to find 
![V=\frac{4}{3}\pi r^3\\\\300=\frac{4}{3}\pi r^3\\\\r^3=\frac{225}{\pi }\\\\r=\sqrt[3]{\frac{225}{\pi }}](/tpl/images/0339/3400/2a8dd.png)
![\frac{dV}{dt}=4\pi r^2 \frac{dr}{dt}\\\\\frac{dr}{dt}=\frac{\frac{dV}{dt}}{4\pi r^2} \\\\\frac{dr}{dt}=-\frac{12}{4\pi (\sqrt[3]{\frac{225}{\pi }})^2} \\\\\frac{dr}{dt}=-\frac{3}{\pi \left(\sqrt[3]{\frac{225}{\pi }}\right)^2}\\\\\frac{dr}{dt}=-\frac{3}{\pi \frac{225^{\frac{2}{3}}}{\pi ^{\frac{2}{3}}}}\\\\\frac{dr}{dt}=-\frac{3}{225^{\frac{2}{3}}\pi ^{\frac{1}{3}}} \approx -0.05537 \:\frac{ft}{h}](/tpl/images/0339/3400/7d703.png)
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Gas is escaping from a spherical balloon at the rate of 12 ft3/hr. at what rate (in feet per hour) i...
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