The radius of a right circular cone is increasing at a rate of 2 inches per seco

Question

The radius of a right circular cone is increasing at a rate of 2 inches per second and its height is decreasing at a rate of 4 inches per second. At what rate is the volume of the cone changing when the radius is 10 inches and the height is 10 inches?

The radius of a right circular cone is increasing at a rate of 2 inches per second and its height is decreasing at a rate of 4 inches per second. At what rate is the volume of the cone changing when the radius is 10 inches and the height is 10 inches?

Explanation / Answer

v=1/3*pi*r^2*h

v'=1/3*pi*(2rr'h+r^2h')

r'=2 h'=-4

v'(10,10)=1/3*pi*(2*10*2*10-100*4)

v'=0

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