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 2 inches per second. at what rate is the volume of the cone changing when the radius is 30 inches and the height is 40 inches?

Answer 1

V=(1/3)πr²h
∴ dV/dt
=(π/3)[r²(dh/dt)+h2r(dr/dt)]
=(π/3)[(30)²(-2)+40(2)(30)(2)]
=(π/3)[-1800+4800]
=1600π in³/sec

Answer: 1600π in³/sec