A cube is shrinking in size in such a way that the volume of the cube decreases at a constant rate of 30 meters cubed per second. How fast is the side length of the cube changing when the area is 1000 meters squared?

We are asked to find the rate at which the side of a cube is decreasing if the volume is decreasing at a steady rate of 30 cubic meters per second at the moment that the surface area of the cube is 100 square meters.
The volume of the cube is given by V=s^3 where s is the side length.
Differentiating both sides with respect to time (t in seconds) we get:
(dV)/(dt)=3s^2(ds)/(dt)
(Here we use the chain rule.)
If the surface area of the cube is 1000 square meters we have:
1000=6s^2 ==> s^2=500/3
With (dV)/(dt)=-30,s^2=500/3 we have:
-30=3(500/3)(ds)/(dt)
==> (ds)/(dt)=-3/50
So the rate of decrease of the side length is -3/50 meters per second.
http://mathworld.wolfram.com/RelatedRatesProblem.html