Spherical Coordinates(r, A, B ) to Cartesian Coordinates( x, y, z ) [ 0-180 degree] Enter r (distance from center) Enter Angle A in Degree Enter Angle B in Degree Find x Find y Find z Find radius of locus of r
Use the formulae-
x=rsinA.cosB
y=rsinA.sinB
z=rcos A

where A is polar coordinate with range [0.π], B is azimuthally coordinate with range [0.2π]
1) r is the distance of the point from centre of sphere which is origin.
2) z-axis makes angle A with r .
3) Projection of r on x-y plane makes an angle B with x-axis.
4) Locus of points of same r making same angle A with z-axis makes a circle parallel to the circle in x-y plane with r as radius .
5) For 360> angle > 180 , use sin(180+A) = - sinA and cos (180 + A ) = - cosA;

(5) Any 4 points satisfying the below determinant condition uniquely describe a sphere.

| x2 +y2+ z2    x     y    z     1|

|x12+y12+z12    x1     y1    z1     1|

|x22+y22+z22    x2     y2    z2     1| = 0

|x32+y32+z32    x3     y3    z3     1|

|x42+y42+z42    x4     y4    z4     1|

(6) vol of sphere / (vol of sphere - vol. of circumscribed cylinder) =2