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?

Printable View

- Mar 28th 2009, 04:38 AMtradarCalc word problem
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? - Mar 28th 2009, 05:47 AMearboth
Let a denote the edge of the cube. Then

$\displaystyle V = a^3$

That means:

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

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

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

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