A) \[80\pi \,\]cu. m/sec
B) \[144\,\pi \,\]cu. m/sec
C) \[80\,\] cu. m/sec
D) \[64\,\] cu. m/sec
E) \[-80\,\pi \] cu. m/sec
Correct Answer: A
Solution :
\[V=\pi {{r}^{2}}h\]; \[\frac{\partial V}{\partial t}=\pi \left[ 2r\frac{\partial r}{\partial t}h+{{r}^{2}}\frac{\partial h}{\partial t} \right]\] \[\frac{\partial V}{\partial t}=\pi \,[2(4)\,(3)\,(6)\,+\,{{(4)}^{2}}(-4)]=\pi \,[144-64]=80\,\pi \text{ }cu\,m/sec\].
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