A) \[2/\pi \]
B) \[1/5\pi \]
C) \[1/10\pi \]
D) \[1/15\pi \]
Correct Answer: B
Solution :
\[\tan \theta =\frac{1}{2}=\frac{r}{h}\] \[r=\frac{h}{2}\] \[V=\frac{1}{3}\pi {{r}^{2}}h\] \[V=\frac{1}{3}\pi .\frac{{{h}^{3}}}{4}\] \[\frac{dV}{dt}=\frac{\pi }{12}{{(3h)}^{2}}\left( \frac{dh}{dt} \right)\] \[5=\frac{\pi }{4}.(100)\frac{dh}{dt}\Rightarrow \frac{dh}{dt}=\frac{1}{5\pi }\]You need to login to perform this action.
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