Solve Weird Depth Problem: Conical Tank Water Flow Rate

[calcatmillbrook]

I've looked everywhere to try to solve this problem and I can't find anything. It is:

A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. If water is flowing into the tank at a rateof 10 cubic feet per minute, find the rate of change of the depth of the water when the water is 8 feet deep.

Thanks for the help.

 

[ice109]

this is a pretty easy related rates problem

 

[HallsofIvy]

Why would you consider that weird? In general, if you can find a formula for volume as a function of height, V(h), then, by the chain rule, dV/dt= (dV/dh) dh/dt. You are given dV/dt and asked to find dh/dt. You need to be able to calculate dV/dh. Do you know (or can you look up) the formula for volume of a cone in terms of radius and height? Here you are told that the tank itself has height 12 feet and radius 5 feet. Do you see that any "cone of water" contained by that tank will have h/r= 12/5?

 

[calcatmillbrook]

sorry, i just started rates on friday

 

[HallsofIvy]

Good! Then you should know exactly how to do this!