Answer
$16\pi t^2$.
Work Step by Step
We know that the surface area of the spherical balloon is the surface area of a sphere, $A=4\pi r^2$. The radius is increasing at $2~cm/s$, so we can write $r=2t$. We plug in $r$ into the area formula to get:
$A=4\pi(2t)^2=16\pi t^2$.
