Calc word problem

**tradar** · March 28th 2009, 04:38 AM

All edges of a cube are expanding at a rate of 3 centimeters per second.
(a) How fast is the volume changing when each edge is 4 centimeter(s)?

(b) How fast is the volume changing when each edge is 9 centimeters?

**earboth** · March 28th 2009, 05:47 AM

Originally Posted by tradar

All edges of a cube are expanding at a rate of 3 centimeters per second.
(a) How fast is the volume changing when each edge is 4 centimeter(s)?

(b) How fast is the volume changing when each edge is 9 centimeters?

Let a denote the edge of the cube. Then

$V = a^3$

That means:

$\dfrac{dV}{dt} = 3a^2 \cdot \dfrac{d a}{dt}$

You already know $a = 4\, cm\, \text{and } \dfrac{d a}{dt} = 3 \frac{cm}s$

I've got $\dfrac{dV}{dt} = 144\,\frac{cm^3}{s}$

b) has to be done in just the same way. I leave this part for you.

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