Posted by My Name Is Bob on Sunday, May 13, 2012 at 2:15pm.
A hitech 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 hitech ball to the nearest tenth?

Math  MathMate, Sunday, May 13, 2012 at 3:19pm
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
=(1³0³):(3³1³):(4³3³)
=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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