on areas

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the surface area of the three faces having the same border of a cuboid are 4,10,40 sq.cm respectively. find the volume of the cuboid?

  • on areas -

    let the dimensions of the cube be x, y , and z
    xy = 4, (#1)
    xz=10 and (#2)
    yz=40 (#3)

    #1 รท #2 :
    z/y = 5/2
    y = 2z/5

    In #3: yz=40 ---> (2/5)z^2 = 40
    z^2 = 100
    z = 10
    then y = (2/5)(10)
    y = 4
    in #1
    xy=4
    4x = 4
    x = 1

    volume = xyz = 1 x 4 x 10 = 40

    check:
    xy = 1x4 = 4
    xz = 1x10 = 10
    yz = 4x40 = 40

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