Related Rates Problem?

Question

You have a bag of cubical balloons that you inflate at a rate of 40cm^3 per second, how fast will the balloon's surface area get larger when the balloons edges are 4cm long?

I have trouble solving things implicitly so any help on this would be appreciated.

Answer 1

Each side of the ballon has an area of x^2 where x is the length of a side. There are 6 sides to a cube. So the total surface area is 6x^2.
A = 6x^2
The volume of the balloon is V = x^3.
You are given dA/dt and want dV/dt.
Solve for x in the volume equation and substitute it in the area equation. Then take the derivative of this with respect to t to get dA/dt in terms of x and dV/dt
It is easy from there