214k views
4 votes
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.

User TAGraves
by
7.8k points

1 Answer

3 votes

Answer:


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

User Arthur Skirvin
by
7.4k points

No related questions found