volume of a cube versus side length


by emma3001
Tags: cube, length, versus, volume
emma3001
emma3001 is offline
#1
Apr14-08, 06:38 PM
P: 42
Show that the rate of change of the volume of a cube with respect to its edge length is equal to half the surface area of a cube.

I know that surface area= 6l^2(because of the six faces)
I know that volume is l^3. How do I relate volume then to edge length
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Pere Callahan
Pere Callahan is offline
#2
Apr14-08, 07:19 PM
P: 588
Quote Quote by emma3001 View Post
Show that the rate of change of the volume of a cube with respect to its edge length is equal to half the surface area of a cube.

The "rate of change" is the derivative.

So what is the derivative of the volume with respect to the edge length?
emma3001
emma3001 is offline
#3
Apr14-08, 07:21 PM
P: 42
Thanks! I now realize that the first derivative of the volume is 3l^2, which is half the surface area

Pere Callahan
Pere Callahan is offline
#4
Apr14-08, 07:24 PM
P: 588

volume of a cube versus side length


Right.


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