A sphere has a radius of 10 cm. A right circular cone has a height of 10 cm and base diameter of 10 cm. The sphere and the cone stand on a horizontal surface. If a horizontal plane cuts both the sphere and the cone, the cross-sections will both be circles.

Find the height of the horizontal plane (from the bottom) (in cm) that gives circular cross-sections of the sphere and cone of equal area.

(In reply to solution by Charlie)

Charlie, Once again thanks for the feedback. I very much appreciate it. I did have a little trouble getting the root of my equation right, and I corrected that in my posted answer. But, as for the geometry, I think I had that OK. Please see: picture

Edited on September 7, 2018, 2:40 pm

Posted by Steven Lord on 2018-09-07 14:34:46