A) \[10\,\pi \]
B) \[100\,\pi \]
C) \[200\,\pi \]
D) \[50\,\pi \]
Correct Answer: C
Solution :
Let r be the radius of spherical balloon. \[\therefore \]Volume, \[V=\frac{4}{3}\pi {{r}^{3}}\] \[\frac{dV}{dt}=\frac{4}{3}\pi 3{{r}^{2}}\frac{dr}{dt}\] \[=4\pi {{r}^{2}}\frac{dr}{dt}\] \[=4\pi {{r}^{2}}\cdot (2)\] \[\left( \because \frac{dr}{dt}=2 \right)\] \[\Rightarrow \] \[\frac{dV}{dt}=8\pi {{r}^{2}}c{{m}^{3}}/min\] Now, when r = 5 cm \[\therefore \frac{dV}{dt}=8\pi {{(5)}^{2}}=200\,\pi \,c{{m}^{3}}/min\]
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