Question #1211a
1 Answer
The volume of a cone is given by
v = 1/3r^2pih
Since
v = 1/3r^3pi
Taking the derivative with respect to time, we have:
(dv)/(dt) = pir^2((dr)/dt)
10 = 25pi((dr)/dt)
2/(5pi)= (dr)/(dt)
This is the rate at which the radius is changing. Since
(dA)/(dt) = 2r(dr)/(dt)pi
(dA)/(dt) = 10(2/(5(pi)))pi
(dA)/(dt) = 4"ft"^2/"min"