- #1

Michele Nunes

- 42

- 2

## Homework Statement

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 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.

## Homework Equations

## The Attempt at a Solution

Okay so I'm using the equation for the volume of a cone to relate the variables of volume and height:

*V*= (1/3)π

*r*, now I only want the variables for volume and height to be in the equation so I have to rewrite the radius

^{2}h*r*in terms of the height

*h*which is where I'm unsure. I think that I should replace

*r*with (5/12)

*h*however someone else doing the problem replaced it with (12/5)

*h*but I don't think that makes sense because you're saying the radius is 12/5 of the height which means it's bigger, however it's not, the radius is much smaller than the height which is why I think (5/12)

*h*seems more logical. But once I rewrite

*r*in terms of

*h*, I've got the hang of it from there, it's just this one step that I'm unsure about.