Related rates problem (involving a cone)

[Pupil]

Homework Statement

Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. The height of the pile is increasing at a rate of ____ feet per minute when the pile is 11 feet high.

Recall that the volume of a right circular cone with height h and radius of the base r is given by (1/3)*pi*(r^2)*h.

Homework Equations

Noted above.

The Attempt at a Solution

I don't understand the problem. If the radius and the height are always the same how can they change?

EDIT: if I am thinking of this correctly then the answer would be 0 (which is incorrect).

 

[Dick]

It's saying the diameter and the radius both vary with time but are always equal at any given time. I.e. r=h. It isn't saying they are always the same in the sense that they are constant. Try and make an attempt again.

 

[Pupil]

It's saying the diameter and the radius both vary with time but are always equal at any given time. I.e. r=h. It isn't saying they are always the same in the sense that they are constant. Try and make an attempt again.

Oh! That makes things much clearer! Thanks!

 

[wkmotley]

It's saying the diameter and the radius both vary with time but are always equal at any given time. I.e. r=h. It isn't saying they are always the same in the sense that they are constant. Try and make an attempt again.

Point of clarification: The problem says the diameter and HEIGHT vary with time, but they are equal to each other. So d = 2r = h, or r = 0.5h.