Center is c and radius is r.
Surface Area S = 4πr2
Volume V = (4/3)*2πr3
Closest point on a sphere
q is the point.
d is the vector between c and q.
q' = q + (||d|| - r / ||d||)*d
If ||d|| < r then point q is inside the circle.
Intersection of two spheres.
d is the vector between spheres centers.
If ||d|| < r1 +r2 then spheres intersect.
A Sphere-Sphere Sweep Test - 1999
Uniform points in sphere and capped cone