Around hole is drilled through the center of a spherical solid of radius r. the resulting cylindrical hole has a height of 4 cm.

a.) what is the volume of the solid that remains?

b.) what is unusual about the answer?

A) If a is the radius of the drilled hole, then r^2 = a^2 + 2^2. If we let a -> 0, then r -> 2. Therefore, the volume of solid that remains is (4/3)*�*r^3 or 32*�/3 cm^3.
b) The answer is independent of the radius r. Although r must be greater than 2.