
#1
Apr1408, 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 



#2
Apr1408, 07:19 PM

P: 588

The "rate of change" is the derivative. So what is the derivative of the volume with respect to the edge length? 



#3
Apr1408, 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




#4
Apr1408, 07:24 PM

P: 588

volume of a cube versus side length
Right.



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