A) \[\frac{1}{30\pi }ft/\min \text{.}\]
B) \[\frac{1}{15\pi }ft/\min \text{.}\]
C) \[\frac{1}{20}ft/\min \text{.}\]
D) \[\frac{1}{25}ft/\min \text{.}\]
Correct Answer: A
Solution :
Given that \[dV/dt=30f{{t}^{3}}/min\] and \[r=15ft\] \[V=\frac{4}{3}\pi {{r}^{3}};\]\[\frac{dV}{dt}=4\pi {{r}^{2}}\frac{dr}{dt}\] \[\frac{dr}{dt}=\frac{dV/dt}{4\pi {{r}^{2}}}=\frac{30}{4\times \pi \times 15\times 15}=\frac{1}{30\pi }\]ft/min
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