This is equivalent to the volume of the N-1 solid which comprises the boundary of an N-Sphere.
The volume of a ball is the easiest formula to remember: It's
.
The only hard part is taking the factorial
of a half-integer. The real definition is that 
, but
if you want a formula, it's:
To get the surface area, you just differentiate to get
.
There is a clever way to obtain this formula using Gaussian
integrals. First, we note that the integral over the line of
is 
. Therefore the integral over N-space of
is 
. Now we change to
spherical coordinates. We get the integral from 0 to infinity
of 
, where V is the surface volume of a sphere.
Integrate by parts repeatedly to get the desired formula.
It is possible to derive the volume of the sphere from ``first principles''.