Question

Coffee is coming out from a conical filter, with height and diameter both are $15\text{cm}$ into a cylindrical coffee pot with a diameter $15\text{cm}$. The rate at which coffee comes out from the filter into the pot is $100{\text{cm}}^3/\text{min.}$

The rate (in $\text{cm/min}$) at which the level of coffee in the pot is rising at the instance when it is $10\text{cm}$, is equal to

• A. $\frac{16}{9\pi }$
• B. $\frac{5}{3\pi }$
• C. $\frac{9}{16\pi }$
• D. $\frac{4}{3\pi }$

Answer 1

The correct option is A $\frac{16}{9\pi }$

For a cylindrical pot, $V=\pi r^{2}h$
$\Rightarrow \frac{dV}{dt}=\pi \left[r^2\frac{dh}{dt}\right]$
$\{\because r=\text{constant}\}$


$\Rightarrow 100=\pi r^2\frac{dh}{dt}$
$\Rightarrow 100=\pi \cdot \frac{225}{4}\cdot \frac{dh}{dt}$
$\Rightarrow \frac{dh}{dt}=\frac{16}{9\pi }\text{cm/min}$