CALC III ANYONE??

Any help is appreciated! In a woodworking project, both Terry and Tony make objects that look like large napkin rings by drilling a hole vertically through the center of a wooden sphere. Each of their final objects has a height of 2 inches, but Terry started with a sphere of radius 4 inches, while Tony's sphere had a radius of just 3 inches. (continued in comments)

Question

CALC III ANYONE??

Any help is appreciated! In a woodworking project, both Terry and Tony make objects that look like large napkin rings by drilling a hole vertically through the center of a wooden sphere. Each of their final objects has a height of 2 inches, but Terry started with a sphere of radius 4 inches, while Tony's sphere had a radius of just 3 inches. (continued in comments)

chosenmatt · Answer

okay?

anonymous · Answer

After they are done, they get into an argument about whose ring has more wood. Terry says that his has more since it is a bigger ring, but Tony says hers has more since it is thicker. Find out how much material is in each ring to settle the argument.

anonymous · Answer

Consider the solid as a solid of revolution, where you are revolving the shaded region below about the x-axis.
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(I had to reconsider something: the drill bit must be changed for the height of both rings to be the same.)