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.

Posted by willow cliffswallow on 2004-09-16 14:51:12