The distance from the center of the sphere to the cross section is R/2.

Then, take a point on the section circle and connect it with the section center and the spherical center to form a triangle with an included angle of 60 degrees.

therefore

R/2× root number 3 = root number 3;

= =》R = 2；

Cubic π of V = 4/3× 2

That is 32π/3.