Page 28 - Standard Handbook Of Petroleum & Natural Gas Engineering

Geometry 17

Spherical wedge bounded by two plane semicircles and a lune (Figure 1-23)

volume of wedge/volume of sphere = u/36Oo
area of lune/area of sphere = u/360°
where u = dihedral angle of the wedge
Regular polyhedra
Name of Solid Bounded By A/ a2 V/aS
Tetrahedron 4 triangles 1.732 1 0.1179
Cube 6 squares 6.0000 1.0000
Octahedron 8 triangles 3.4641 0.4714
Dodecahedron 12 pentagons 20.6457 7.6631
Icosahedron 20 triangles 8.6603 2.1817
where A = area of surface
V = volume
a = edge
Ellipsoid (Figure 1-24)

volume = 4/3 xabc
where a, b, c * semiaxes