# Depth/tank/rate of change problem

1. Feb 23, 2009

### doogerjr

1. The problem statement, all variables and given/known data
A conical tank, (with vertex down) is 10 feet across the top and twelve feet deep. If water is flowing into the tank at a rate of 10 cubic feet per minute, find the rate of change of the depth of the water when the water is 8 feet deep.

2. Relevant equations???

3. The attempt at a solution???

2. Feb 23, 2009

### HallsofIvy

Staff Emeritus
Have you made any attempt to solve this problem at all? Surely, if someone expects you to do this problem, they expect you to know some basic formulas and some concepts of "related rates".

A very relevant equation would be the volume of a cone of radius R and height h. Also, as the water level goes up, both R and h change. Here's my recomendation: draw a picture, a triangle with base (at the top) of length 10ft and altitude (downward) 12 feet. Now draw a horizontal line across the triangle representing the surface of the water. You can get a relation between h and R using "similar triangles". Replace R by that function of h so you have the volume as a function of h only and differentiate to get dV/dt depending on dh/dt.