A) 1 cm/min
B) 2 cm/min
C) 5 cm/min
D) 3 cm/min
Correct Answer: A
Solution :
Given, \[\frac{dv}{dt}=100\pi c{{m}^{3}}/\min \] where, V is the volume of spherical ball. \[\therefore \] \[\frac{d}{dt}\left( \frac{4}{3}\pi {{r}^{3}} \right)=100\pi \] \[\Rightarrow \] \[3{{r}^{2}}\frac{dr}{dt}=\frac{300\pi }{4\pi }\] \[\Rightarrow \] \[{{\left[ \frac{dr}{dt} \right]}_{r=5}}=\frac{300}{4\times 3\times 25}=1\,\,cm/\min \]
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