Question

The radius of a right circular cone is increasing at a rate of 5 inches per second and its height is decreasing at a rate of 3 inches per second. At what rate is the volume of the cone changing when the radius is 50 inches and the height is 20 inches

Answer 1

1700π in³/s

Explanation:

Volume of a cone is expressed as

V = 1/3πr²h

Given

dr/dt = 5in/s

dh/dt = 3in/s

radius r = 50in

h = 20in

Required

dV/dt = ?

dV/dt = dV/dr * dr/dt + dV/dh*dh/dt

dV/dr = 1/3πh (5) + 1/3πr²(2)

dV/dt = 1/3π(20)(5)+1/3 π(50)²(2)

dV/dt = 100π/3 + 5000π/3

dV/dt = 5100π/3

dV/dt = 1700π in³/s