Take a solid cylinder of radius R and height 2R. Remove the right “double cone” which passes through the center of the solid cylinder and extends meet the circular discs on the top and bottom of the cylinder. See Figure 1.
The volume of the remaining object and the volume of a sphere of radius R are the same!
Presentation Suggestions:
Pictures, pictures!
The Math Behind the Fact:
Using Cavalieri’s principle is perhaps the most effective way to prove this in a multivariable calculus course.
How to Cite this Page:
Su, Francis E., et al. “Right Double Cone.” Math Fun Facts. <https://www.math.hmc.edu/funfacts>.
Fun Fact suggested by:
Jorge Aarao