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Express the edge length of a cube as a function of the cube's diagonal length d. Then express the surface area and volume of the cube as a function of the diagonal length.

  • pre-calculus -

    d^2 = 3s^2
    so, s = (d/3)^(1/2)
    v = s^3 = (d/3)^(3/2)
    A = 6s^2 = 2d

  • pre-calculus -

    edge length s
    diagonal of a side = s sqrt 2
    then right triangle with legs s and s sqrt 2
    d^2 = s^2 + 2 s^2 = 3 s^2
    d = s sqrt 3

    s = d/ sqrt 3 = d (3)^-.5

    area = 6s^2 = 6d^2 (3)-1 = 6d^2/3 =2 d^2

    vol=s^3=[d(3^-.5)]^3 = d^3 /(3 sqrt 3)
    = (d^3 sqrt 3)/9

  • pre-calculus - typo -

    Scratch all that, since

    s = d/√3
    v = s^3 = d^3/√27
    a = 6s^2 = 2d^2

  • pre-calculus -

    whew :)

  • pre-calculus -

    thank you :)

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