A) \[\frac{1}{6}\]
B) \[\frac{1}{9}\]
C) \[\frac{1}{36}\]
D) \[\frac{1}{24}\]
Correct Answer: C
Solution :
Volume of sphere \[V=\frac{4}{3}\pi {{r}^{3}}\] ?(1) \[\frac{dv}{dt}=\frac{4}{3}.3\pi {{r}^{2}}.\frac{dr}{dt}\] \[4\pi =4\pi {{r}^{2}}.\frac{dr}{dt}\] \[\frac{1}{{{r}^{2}}}=\frac{dr}{dt}\] Since, \[V=288\pi \]therefore from (1), we have \[288\pi =\frac{4}{3}\pi ({{r}^{3}})\Rightarrow \frac{288\times 3}{4}={{r}^{3}}\]\[\Rightarrow \]\[216={{r}^{3}}\] Hence, \[\frac{dr}{dt}=\frac{1}{36}.\]
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