Answer
$A[r(t)]=40000\ \pi \ t$
Work Step by Step
The area of a circle is given by the formula:
$A=\pi r^2$
And we have the radius as a function of time:
$r(t)=200\sqrt t.$
Therefore, the composite function will be:
$A[r(t)]=\pi (200\sqrt t)^2=40000\ \pi \ t$
