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Section 15.3: Integration in Polar Coordinates

Exercise 28

  1. A cylindrical drill with radius \(r_1\) is used to bore a hole through the center of a sphere of radius \(r_2\). Find the volume of the ring-shaped solid that remains.
  2. Express the volume in part (a) in terms of the height \(h\) of the ring. Notice that the volume depends only on \(h\), not on \(r_1\) or \(r_2\).