You are blowing air into a spherical balloon at a rate of $\frac{4\pi}{3}$ cubic inches per second. (The reason for this strange looking rate is that it will simplify your algebra a little.) Assume the radius of your balloon is zero at time zero. Let $r(t)$, $A(t)$, and $V(t)$ denote the radius, the surface area, and the volume of your balloon at time $t$, respectively. (Assume the thickness of the skin is zero.) All of your answers below are expressions in $t$:
$r'(t) =$ inches per second,
$A'(t) =$ square inches per second, and
$V'(t) =$ cubic inches per second.
Hint: The surface area $A$ and the volume $V$ of a sphere of radius $r$ are given by $$A = 4\pi r^2 \quad\hbox{and}\quad V = \frac{4\pi r^3}{3}.$$