A round hole is drilled through the center of a spherical solid with a radius (r). The resulting cylindrical hole has height 4 cm.
a)What is the volume of the solid that remains?
b)What is unusual about the answer?
The volume of the sphere is 4/3 pi r^3. The volume of the cylinder is pi(2^2)(2r) = 8pi(r). So the solid that remains is 4/3 pi r^3 minus 8 pi (r). The interesting thing is that 8 pi (r) is the second derivative of 4/3 pi r^3.