 Four out of Eight Octants in a Sphere, radius 1/2:

Exact Area = 5 pi / 4

Approximate Area = 3.9267

Exact Volume = pi / 12

Approximate Volume = 0.2618

 A Roman surface, x^{2}y^{2}+x^{2}z^{2}+y^{2}z^{2}xyz = 0:

Exact Area = ????

Approximate Area = 3.195

Exact Volume = 1 / 6

Approximate Volume = 0.1666

 Four out of Eight Octants in an Octahedron (distance from center
to vertex = 1/2):

Exact Area = (sqrt(3) + 3) / 2

Approximate Area = 2.366

Exact Volume = 1 / 12

Approximate Volume = 0.08333
