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Volume of a cube versus side length

  1. Apr 14, 2008 #1
    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. jcsd
  3. Apr 14, 2008 #2

    The "rate of change" is the derivative.

    So what is the derivative of the volume with respect to the edge length?
  4. Apr 14, 2008 #3
    Thanks! I now realize that the first derivative of the volume is 3l^2, which is half the surface area
  5. Apr 14, 2008 #4
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