Suppose a water bucket is modeled by the frustrum of a cone with height 1 foot and upper and lower radii....?

Question

of 1 foot and 9 inches respectively. It is leaking water from the bottom at a rate of 8 inches cubed per minute. At what rate is the water level falling when the depth in the bucket is 6 inches?

Volume of frustrum:
(pi*h/3)*(R^2+rR+r^2)

Answer 1

V = (1/3) pi h (R^2 + 9R + 81)

R = 0.25 h + 9

Substitute R into the equation for V and then take the derivative with respect to time.

dV/dt = 8 inches cubed per minute, you know h is 6 inches, solve for dh/dt