volume of a cube versus side length

emma3001

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

Pere Callahan

Quote by emma3001

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

Thanks! I now realize that the first derivative of the volume is 3l^2, which is half the surface area

Pere Callahan

Right.

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emma3001	volume of a cube versus side length Tweet 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

Pere Callahan	volume of a cube versus side length Right.