Hi! Please take a look at the extract from my book. In the marked paragraph, they assumed that for any consideration, the amount of charge may be considered as centered at the center of the sphere.
They did not mention any exceptions here. But this assumption fails to calculate the potential inside the sphere. According to this, the potential r meters away from the center will be equal to ke/r but in reality it is ke/radius of the sphere. Why is it so?
And are there other cases where this assumption fails?
Thanks.

They are talking about the potential at the surface of the sphere, not inside it. For points inside the sphere the electric field = 0, so the potential V at any point inside the sphere is the same as the potential at the surface. Here's a diagram that should make it clear:

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/potsph.html

Thanks. It is clear now.