The rate at which fluid level inside vertical cylindrical tank of radius r drop if we pump fluid out at the rate of 3cm3l/min is

A
$- \frac{1}{π r^{2}}$
B
$\frac{3}{π r^{2}}$
C
$\frac{2}{π r^{2}}$
D
$\frac{4}{π r}$

Solution:

$\begin{array}{l} V = π r^{2} h \Rightarrow \frac{d V}{d t} = π r^{2} \frac{d h}{d t} \\ \Rightarrow \frac{d h}{d t} = - \frac{3}{π r^{2}} \end{array}$

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