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.

Step-by-step 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