The centroid is the centre. How you find it depends on what information you have about the hypersphere.

One example is a hypersphere in 4 dimensions. For example, the unit 4 dimensional hypersphere has the equation x^2+y^2+z^2+w^2=1 but you can not easily graph this. We can replace 1 for r^2 for the general hypersphere and we could replace each x, y,z and w for (x-a), (y-b), (z-c) and (w-d) to place the center of the sphere at points (a,b,c,d) If you took slices of it, they would be 3d spheres. We can write equations for 4 or any dimension figure and we can deal with them mathematically, we just can't see them in our mind's eye. Pi^2/2 x R^2 is the formula for the volume of the 4 d hypersphere. Another way to think of it is to move the sphere through space. At time t=0 the sphere is at location 0 and t=1 at another location. We can think of t as the fourth dimension. (Sounds like the twilight zone?)

It is the radius of a circle or of a sphere

exponential functions, circles (area, perimeter, etc.), round objects in general (circle, sphere, hypersphere, etc.

of a circle: pi*(r^2)

of a sphere: (surface area) 4*pi*(r^2)

of a hypersphere: ... ?