Question

The radius of a right circular cone is increasing at a rate of 1.1 in/s while its height is decreasing at a rate of 2.4 in/s. At what rate is the volume of the cone changing when the radius is 109 in. and the height is 198 in.

Answer 1

`79591.8872 in^3/s`

Explanation:

we know that the volume of a right circular cone is give as

`V(r,h)= (1)/(3) \pi r^2h\\\\`

Therefore differentiating partially with respect to r and h we have

`(dV)/(dt) = (1)/(3)\pi [2rh(dr)/(dt) +r^2(dh)/(dt)]`

`(dV)/(dt) = (\pi)/(3) [218*198*1.1+109^2*2.4]`

`(dV)/(dt) = (\pi)/(3) [47480.4+28514.4]\\\\(dV)/(dt) = (\pi)/(3) [75994.8]\\\\ (dV)/(dt) = 3.142 [25331.6]\\\\ (dV)/(dt) =79591.8872 in^3/s`