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A hi-tech bowling ball is constructed from concentric spheres, kind of like a perfectly round M&M peanut. The inner sphere, of material X, has a radius of 1 inch. The middle spherical shell of material Y has a thickness of 2 inches. The outer shell of material Z has a thickness of 1 inch. A ball of the same size made of 100% X,Y, or Z weighs 16, 14, and 12 lbs respectively. What is the weight of this hi-tech ball to the nearest tenth?

  • Math -

    The volume of a sphere is
    (4π/3)r³

    The shell thicknesses are:
    X=1", Y=2", Z=1"



    The proportions of volumes X, Y and Z are:
    X:Y:Z
    =(1³-0³):(3³-1³):(4³-3³)
    =1:8:55

    Therefore weight of ball
    =(1*16+8*14+55*12)/(1+8+55)
    =788/64
    =197/16
    =12 5/16 pounds (12 lb 5 oz)

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