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Volume of a cube versus side length

  • Thread starter emma3001
  • Start date
42
0
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
 

Answers and Replies

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?
 
42
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Thanks! I now realize that the first derivative of the volume is 3l^2, which is half the surface area
 
Right.
 

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