Solving problem using derivative

**hejmh** · January 9th 2011, 03:55 AM

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?

Solving problem using derivative-dsc-0000170.jpg

Thanks for your help.

**BAdhi** · January 9th 2011, 04:16 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 $\frac{dh}{dt}$ .

**alexmahone** · January 9th 2011, 04:19 AM

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?

Click image for larger version.

Name: DSC-0000170.jpg
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Thanks for your help.

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

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

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

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

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