# Solving problem using derivative

• Jan 9th 2011, 04:55 AM
hejmh
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?
Attachment 20367

• Jan 9th 2011, 05:16 AM
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, $\frac{dV}{dt}$ and $\frac{dh}{dt}$ (h is the height).
you know h, $\frac{dV}{dt}$. substitute and find $\frac{dh}{dt}$.
• Jan 9th 2011, 05:19 AM
alexmahone
Quote:

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?
Attachment 20367

$r=\frac{h}{2}$
$V=\frac{1}{3}\pi r^2h=\frac{1}{3}\pi (\frac{h}{2})^2h=\frac{1}{12}\pi h^3$
$\frac{dV}{dt}=\frac{1}{4}\pi h^2\frac{dh}{dt}$
Now just substitute the given values to find $\frac{dh}{dt}$.