Question #1211a

1 Answer
May 9, 2017

The volume of a cone is given by

v = 1/3r^2pih

Since r= h always, we have:

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 A = r^2pi

(dA)/(dt) = 2r(dr)/(dt)pi

(dA)/(dt) = 10(2/(5(pi)))pi

(dA)/(dt) = 4"ft"^2/"min"