The surface area of the ice cube is decreasing at the rate of 10cm^2/sec. At what rate the volume of the cube is changing when the area is 14cm^2?

Please explain thoroughly I have a test in 2 hours!

Question

The surface area of the ice cube is decreasing at the rate of 10cm^2/sec. At what rate the volume of the cube is changing when the area is 14cm^2?

Please explain thoroughly I have a test in 2 hours!

anonymous · Answer

you need a formula relating the surface area of a cube to the volume

anonymous · Answer

that is the only hard part
a quick calculation gives $$S=6\sqrt[3]{V}^2$$ or better for calculus 
$$\huge S=6V^{\frac{2}{3}}$$

anonymous · Answer

that makes 
$$S'=4V^{-\frac{1}{3}}V'$$ plug in the numbers, solve for $V'$

anonymous · Answer

Sorry was watching Israel PM speech! Thanks for the help