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AP® Calculus AB-BC

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Difficult

Surface Area of a Cube

APCALC-BODS1E

The surface area of a cube is increasing at a rate of $10\, \frac {\text{cm}^2}{\text{sec}}$.

How fast is the volume of the cube increasing when each edge of the cube is $5\ \text{cm}$?

A

$750\, \cfrac {\text{cm}^3} {\text{sec}}$

B

$75\, \cfrac {\text{cm}^3}{\text{sec}}$

C

$\cfrac{125}{2}\, \cfrac {\text{cm}^3}{\text{sec}}$

D

$\cfrac{25}{2}\, \cfrac {\text{cm}^3}{\text{sec}}$