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"#