Homework SourseThe radius of a right circular cone is increasing at a rate
The radius of a right circular cone is increasing at a rate of 8 inches per minute, and the height is decreasing at a rate of 6 inches per minute. What are the rates of change of the volume and surface area when the radius is 12 inches and the height is 36 inches?
Find Rate of change for volume and
Rate of change of the surface area
Find Rate of change for volume and
Rate of change of the surface area
Solution
V = 1/3 r^2h
dV/dt = dV/dr * dr/dt + dV/dh * dh/dt = (2/3 rh)*(8) + (1/3 r^2)*(-6) =
(2/3 * 12*36*8 - 6/3 *12*12 ) = 2016 inch^3/min
