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.