Thread: Solving problem using derivative

There is a coffee mashin (picture in the attachment )which coffee is falling from the filter to a cylinder with speed of 150 cm^3/min.
How much is the speed of decreasing the heigh of coffee in the filter when the height is 12.5 cm in the filter?


Thanks for your help.

get an equation for the volume of the liquid in the filter with height as the variable.

differentiate volume with respective to the time. then you'll get an expression with h, $\displaystyle \frac{dV}{dt}$ and $\displaystyle \frac{dh}{dt}$ (h is the height).
you know h, $\displaystyle \frac{dV}{dt}$. substitute and find $\displaystyle \frac{dh}{dt}$.

Originally Posted by hejmh

There is a coffee mashin (picture in the attachment )which coffee is falling from the filter to a cylinder with speed of 150 cm^3/min.
How much is the speed of decreasing the heigh of coffee in the filter when the height is 12.5 cm in the filter?


Thanks for your help.

$\displaystyle r=\frac{h}{2}$

$\displaystyle V=\frac{1}{3}\pi r^2h=\frac{1}{3}\pi (\frac{h}{2})^2h=\frac{1}{12}\pi h^3$

$\displaystyle \frac{dV}{dt}=\frac{1}{4}\pi h^2\frac{dh}{dt}$

Now just substitute the given values to find $\displaystyle \frac{dh}{dt}$.