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 attempted solution by Steven Lord)

Your equations assume the center of the sphere is at the same level as the base of the cone. The center of the sphere is actually at the same level as the apex of the cone.

Edited on September 7, 2018, 2:07 pm

Posted by Charlie on 2018-09-07 14:05:47