A) \[\frac{1}{6}\]
B) \[\frac{1}{9}\]
C) \[\frac{1}{24}\]
D) \[\frac{1}{36}\]
Correct Answer: D
Solution :
\[V=\frac{4}{3}\,\pi {{r}^{3}}\] Now, \[\frac{dV}{dt}=4\pi {{r}^{2}}\,\frac{dr}{dt}\] \[\Rightarrow \,\,4\pi =4\pi {{r}^{2}}\,\frac{dr}{rt}\] \[\therefore \,\,\frac{dr}{dt}\,=\frac{1}{{{r}^{2}}}\,=\frac{1}{36}\] As \[V=288\,\pi \Rightarrow \,\,r=6\]You need to login to perform this action.
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