prove that total volume of universe is 2(pi)^2R^3where R is the radius of universe curvature.?

Answer 1

Don't you mean 1/2 (pi)^2 R*4 ? That's the volume of a 4D hypersphere.

2 (pi)^2 R^3 would be the 3D "surface area" of this 4D hypersphere

Deriving either one here is a slightly ambitious use of the little space here.