related rates - volumes

Question

An inverted cone has a height of 11 inches and an initial radius of 18 inches. The volume of the inverted cone is decreasing at a rate of 541 cubic inches per second, with the height being held constant. What is the rate of change of the radius, in inches per second, when the radius is 5 inches?

Answer 1

The volume of a cone is needed [ V=(1/3)(π)(r²)(h) ]. Taking the derivative of this formula with respect to time. Then from there, plug in all known variables and solve for the rate of change of the radius (dr/dt).

Answer 2

The Volume of a cone is

V = π r² h / 3

We are told that h is held constant. Hence

dV/dt = (2/3) π r h dr/dt

dr/dt = (3/2) (dV/dt) / (π r h) = (3/2) ( -541) / (π*5*11) = -4.6965 in/sec, ans.

Notice that we did not require the initial value of the radius, 18.