Volume of a cube versus side length

  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. The "rate of change" is the derivative.

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