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?
I think nikki nailed it. At first glance, I thought that the missing radius of the hole would be needed for a solution.
I find it interesting that the Pythagoren Theorem allows us to express
the radius of the hole in terms of the given height of the hole and the
radius of the sphere.
What blows my mind is that in working the equations to find the
remaining volume, all of the radius terms cancel out, leaving only the
simple formula based only on the given hole height.
I can see and follow nikki's solution, but a part of me still doesn't want to believe it.
Pythagorean Theorem
