Let these three points be A, B and C, the center of the small circle is P, the center of the ball is O, the radius of the small circle is R, and the radius of the ball is R. ..

The area of a small circle passing through three points is equal to twice the perimeter ratio,

Then the radius of the small circle r=PA=PB=PC= root number 2.

The spherical distance between any two points is equal to 1/4 of the circumference of the great circle.

Then angle AOB= angle BOC= angle COB=90 degrees.

AB=BC=CA=R* radical number 2

Because AB=PA* radical number 3= radical number 2* radical number 3

(Triangle PAB is an isosceles triangle, the top angle is 120 degrees, and the bottom is the root sign three times the waist length. )

R* radical number 2= radical number 2* radical number 3

R= root number 3

The volume of the ball V=4/3* pie * r 3 = 4 * root number 3* pie.