+382 A perfect sphere is inscribed inside a right circular cone (60 degrees vertex). Find the ratio of the volume of the sphere to the cone.
Let r be the radius of the sphere. Then the volume of the sphere is 4/3*pi*r^3 and the voluem of the cone is 1/3*pi*(2r)^2*3r = 4*pi*r^3, so the ratio is 1/3.
