This link describes a method for determining the most probable radius of an electron for a Hydrogen atom in the ground state.
It states that :
The radial probability density for the hydrogen ground state is obtained by multiplying the square of the wavefunction by a spherical shell volume element.
When I went to solve this problem myself I multiplied the square of the given wavefunction by the volume of a sphere, which gave me the wrong answer as I know it should be the Bohr radius.
When I thought about this problem it seemed reasonable to multiply it by the volume of a sphere rather than the surface area of a sphere (my gut feeling). The link doesn't really explain to me why it uses a surface area and not a volume of a sphere and I would like some help in getting an intuition for why the surface area is used and gives the right answer and the volume of a sphere does not.