related rates sphere volume and area calculus problem I  have been given the following problem: 
A spherical balloon is expanding at the rate of 60 pie in^3/sec. How fast is the surface area of the balloon expanding when the radius of the balloon is 4 inches? 
I don't understand how the way I set the problem up is not giving me the correct answer. I have created an equation that links volume to area, did implicit diff. and now I should have only 2 variables, one of which I have the value for, dV/dt.  please see image for how I set up the problem 

We have that $$\frac{\mathrm dV}{\mathrm dt} = 4 \pi r^2\cdot \frac{\mathrm dr}{\mathrm dt} =60$$
which implies $$\frac{\mathrm dr}{\mathrm dt} =\frac{60}{4 \pi r^2}$$
We know that $A = 4 \pi r^2$, and so we also have
$$\frac{\mathrm dA}{\mathrm dt} = 8\pi r\cdot \frac{\mathrm dr}{\mathrm dt} $$
Plug in what we found for $\frac{\mathrm dr}{\mathrm dt}$ and plug in $r=4$ to get
$$\frac{\mathrm dA}{\mathrm dt} = 8\pi r\cdot \bigg( \frac{60}{4 \pi r^2}\bigg) $$
$$\frac{\mathrm dA}{\mathrm dt} = \frac{120}r = \frac{120}4$$
$$\frac{\mathrm dA}{\mathrm dt} = 30$$
