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?

Answer 1

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)