Question 1203952


The area of a circle with respect to its radius can be modeled using the following function:

{{{A(r) = pi*r^2}}}

The derivative of this function is as follows:

{{{A}}} '{{{ (r) = 2pi*r}}}


Therefore, the instantaneous rate of change of the area of a circle when the radius is {{{3 }}}centimeters can be found by calculating {{{A}}} ' {{{(3)}}}.


{{{A}}} ' {{{(3) = 2pi(3) = 6pi }}}≈ {{{18.85}}}

We get that the instantaneous rate of change of the area of a circle when the radius is {{{3 }}}centimeters is approximately {{{18.85}}} area square centimeters per radius centimeter.