A) \[80\text{ }\pi \text{ }cu\text{ }m/s\]
B) \[\text{144 }\pi \text{ }cu\text{ }m/s\]
C) 80 cu m/s
D) 64 cu m/s
E) \[-\text{ }80\text{ }\pi \text{ }cu\text{ }m/s\]
Correct Answer: A
Solution :
Let h and r be the height and radius of cylinder. Given that\[\frac{dr}{dt}=3m/s,\frac{dh}{dt}=-4m/s.\] Also, On differentiating w.r.t. t \[\frac{dV}{dt}=\pi \left[ {{r}^{2}}\frac{dh}{dt}+h.2r\frac{dr}{dt} \right]\] At \[r=4m\text{ }and\text{ }h=6m\] \[\frac{dV}{dt}=\pi [-64+144]=80\pi \,cu\,m/s\]
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