Hi Tracy.

1) Find the relationship between the quantities.

The involved quantities are volume and height in your question. So we turn to the equation for the volume of a cone: V = 1/3 (pi) r² h. Since the radius of the base always equals half the height, we have r = (h/2), so the equation for the volume becomes V = h³ / 12.

2) Differentiate the equation with respect to time. This will relate the rates. This means you differentiate both sides of the equation:

dV/dt = d(h³/12)/dt

dV/dt = (1/12) d(h³)/dt

dV/dt = 3h²/12 (dh/dt) <-- remember that the chain rule applies!

dV/dt = h² / 4 (dh/dt)

3) Substitute in the values you know are given in the question. dV/dt is the rate of change of the volume. That's 10 cubic feet/minute. h is the height: 5 ft. dh/dt is the rate of change of the height, which is what you are asked for. So we simply plug them in and solve for dh/dt:

10 = 5² / 4 (dh/dt)

dh/dt = 40 / 25

dh/dt = 1.6 ft / minute

Hope this helps. In the future, let us know where you are stuck on a problem, rather than just sending the question.
Stephen La Rocque.