Question #1211a

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Answer 1 · 2017-05-09T18:36:24

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"#