A right circular cone of height h is cut by a plane parallel to the base at a distance h/3 from the base, then the volumes of the resulting come and the frustum are in the ratio?

The volume of the original cone is V = (πR²h)/3
The height and the radius of the smaller cone are 2h/3 and 2R/3, respectively
⇒ 1/3π (2R/3)² x 2h/3 = 8V/27
∴ Volume of the frustum = (V - 8V/27) = 19V/27
So, the required ratio is 8 : 19 .