A) 1 cm/min
B) 2 cm/min
C) \[\frac{1}{376}cm/min\]
D) 5 cm/min
E) 3 cm/min
Correct Answer: A
Solution :
Given, \[\frac{dV}{dt}=100\pi \,c{{m}^{3}}/\min \] \[\therefore \] \[\frac{d}{dt}\left( \frac{4}{3}\pi {{r}^{3}} \right)=100\pi \] \[\Rightarrow \] \[3{{r}^{2}}\frac{dr}{dt}=\frac{300\pi }{4\pi }\] \[\Rightarrow \] \[{{\left( \frac{dr}{dt} \right)}_{(r=5)}}=\frac{300}{4\times 3\times 25}\] \[=1\text{ }cm/min\]
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