If the volume of a cube is increasing at $\displaystyle 24 in^3/min$ and the surface area of the cube is increasing at $\displaystyle 12in^2/min$

, what is the length of each edge of the cube?

A. 2

B$\displaystyle 2 \sqrt{2}$

C. $\displaystyle 12^{1/3}$

D. 4

E. 8

Answers are in inches.

This is what I know:

Dv/dt= 24

and DSA/dt= 12

$\displaystyle v= s^3$

SA= 3s...I think

So,

Dv/dt= 3s ds/dt

dSA/dt= 2 ds/dt

Ds/dt= $\displaystyle \frac{dv/dt}{3s}$

Now what?

Thanks!