Question

The radius of a right circular cone is increasing at a rate of 1.6 in/s while its height is decreasing at a rate of 2.2 in/s. At what rate is the volume of the cone changing when the radius is 135 in. and the height is 135 in.

Answer 1

Explanation:

let radius=r

height=h

dr/dt=1.6 in/s

dh/dt=-2.2 in/s

volume v=1/3 πr²h

dv/dt=1/3 π[h*2r×dr/dt+r²×dh/dt]

when r=135 in

h=135 in

dv/dt=1/3 π[2×135×135×1.6+135²×(-2.2)]

=1/3 π[135²(3.2-2.2)]

=1/3π135²×1

=6075 π in³/s