# Simanek

• February 17, 2020

The “Holey” Sphere

[From the website of Dr. Donald Simanek—see further down.] Browsing Martin Gardner’s books I stumbled on this diabolical puzzle. Gardner calls it “an incredible problem”. He traces it back too Samuel I. Jones’ Mathematical Nuts, 1932, p. 86. It is seen on the web in various forms, often ambiguous in wording, along with endless discussions often leading nowhere. I have tried to restate it to remove ambiguity (which isn’t easy). A hole is drilled completely through a sphere, directly through, and centered on, the sphere’s center. The hole in the sphere is a cylinder of length 6 inches. What is the volume of the remainder of the sphere (not including the material drilled out). You’d think there’s not enough information given. But there is. The solution does not require calculus. Gardner gives an insightful solution that requires only two sentences, including just one equation. Visit From mathworld.wolfram.com for more info. The answer is provided by Doctor Donald Simanek, Professor of Physics Emeritus at Lockhaven University. Visit Donald Simanek’s page at Lockhaven.edu for more brain-bending physics puzzles! Now that’s an interesting answer! Keep scrolling down… Wanna see a video answer to the brainteaser? This video was created by Tom McNaney Jr., Generalist Applications Engineer, Fellow at PTC (the company that I currently work for). Here is his detailed approach to the brainteaser using PTC’s flagship CAD program Creo Parametric! For the Holey Sphere challenge, Creo Parametric says the volume is 113.097 in^3. Interestingly, the volume remains constant regardless of the sphere Radius. Cool. I have no idea what the mathematical formula is, but probably 4/3*Pi*(something)^3. Who needs advanced math when they have Creo or Mathcad?