Well, where ever you got that formula should tell you what "p" is- but I don't recognize that formula.

Here is how I would do that problem. First, because of the spherical symmetry, I would use spherical coordinates to get parametric equations for the sphere. Taking in spherical coordinates, , , and .

That is, we can write the "position vector" for any point on the sphere as

The derivatives with respect to the parameter are vectors in the tangent plane at each point:

.

The cross product of those two vectors, the "fundamental vector product" for the surface, is normal to the surface at each point and, in fact, gives the vector "differential of suface area:

(Of course, changing the order in which you take the cross product changes the sign: . We know each component is "+" because the problem specifically says "in the direction away from the origin")

The flux of any vector function across that sphere is the integral of the dot product of the vector function with that vector

Your function is so you should find that the and terms cancel and your integral is

which is very easy.

Because of the symmetry here, the answer should not be too surprizing.