Name: Nicole
Who is asking: Student
Level of the question: Secondary

Question: I would like to know how I could find the volume underneath the Mitchell Park Domes? The Diameter of the Domes is 140ft, 85ft high and 15,000 square feet.

Hi Nicole.

The Mitchell Domes in Milwaukee aren't geodesic domes (which means cut off of a sphere). They are beehive shaped, which is closer to being a paraboloid than a spherical section. The area you provided is really dependent on the internal layout (the floors) so it doesn't really factor into our thinking.

A paraboloid is a three dimensional shape whose cross-sectional shape is a parabola (just like the cross-section of a geodesic dome would be a circular arc).

The volume formula (which you can derive with just a tiny bit of calculus) is simply
V = (pi/2) r2 h
where r is the radius and h is the height. Use your figures to come up with a volume estimate, but remember that a beehive shape looks sort of paraboloid, but I'm not sure that's in the blueprints!

Stephen La Rocque>