# Thread: Related rates problem

1. ## Related rates problem

Hello, i'm not exactly sure how to do this one.

Water is draining for a conical filter into a cylindrical cup at the rate of 10 cubic centimeters per minute. The conical filter measures 10 cm tall and 10 cm across its top. The diameter of the cylindrical cup is 15 cm.

(a) How fast is the level of water in the filter falling when the water in the filter is 8 cm deep?

(b) At the same time as in part a, how fast is the level of water in the cup rising?

I can somewhat get it, but I need a start and some explanation. Thanks a lot.

2. First you can get by triangle analogies that the radius of the water cone is always half the height. Let h be the heigth of this water cone.
$V = \frac{\pi h^3}{4}$
$\frac{dV}{dh} = \frac{3 \pi h^2}{4}$
$\frac{dh}{dV} = \frac{4}{3 \pi h^2}$
You are given $\frac{dV}{dt} = 10$
$\frac{dh}{dV}\frac{dV}{dt} = \frac{dh}{dt} = 10\frac{4}{3 \pi h^2}$
Replace h by what value you want and be careful that your units are consistent.
Exercice b is quite easier than exercice a