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if you have a large cube with a surface area of 32 and a smaller cube with the surface area of 18 what would the ratio be for the smaller figure to the larger figure

  • math -

    I think you mean, the ratio of the lengths of the smaller and larger cube.
    Recall that the surface area of a cube is given by
    SA = 6s^2
    where s = length of one side
    then we get the length of one side of each cube.
    32 = 6s^2
    16/3 = s^2
    s = 4/sqrt(3)

    18 = 6s^2
    3 = s^2
    s = sqrt(3)

    Finally, we get the ration of smaller length to larger length:
    sqrt(3) / (4/sqrt(3))
    sqrt(3)*sqrt(3) / 4
    3/4 or 3:4

    hopw this helps~ :)

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