Question

Estimate the instantaneous rate of change in the area of a circle when the radius is 3cm? The formula for the area of a circle is A=`pir^2`.

Answer 1

`A=pir^2`
Differentiating with respect to `r` we get the rate of change of `A` with respect to `r` as function of `r`

`A(r)=(dA)/(dr)=2pir`

So the rate of change in the area of a circle when the radius is 3cm will be
`A(3)=[(dA)/(dr)]_(r=3)=2pixx3=6pi` cm