Correction (I think):
[imath]A = \pi r^2[/imath] and [imath]r = 4t[/imath]
So [imath]A = \pi (4t)^2[/imath]
Let [imath]u = 4t[/imath]
[imath]\frac{dA}{dt} = \frac{dA}{du} \times \frac{du}{dt}[/imath]
[imath]\frac{dA}{dt} = \frac{d (\pi u^2)}{du} \times \frac{d(4t)}{dt}[/imath]
[imath]\frac{dA}{dt} = 2\pi u \times 4 = 8 \pi u = 8 \pi \times 4t = 32 \pi t[/imath]
At the 3 m mark, the time is [imath]\frac{3}{4}[/imath] seconds
So at the 3 m mark, [imath]\frac{dA}{dt} = 32 \times \pi \times \frac{3}{4} = 24\pi[/imath] sq. m/second
Correct?
