I have the feeling there are some things missing to solve it? First of all I think the Y is supposed to be a spherical harmonic…but normally the l value is at the bottom and the m value at the top. But this would imply an m > l. But working forwards assuming l=2 and m=0. And assuming the function gives the radius in function of the angle theta (R for radius seems logical). There is still the value of the charge missing. The previous examples all had “+” for charge, but this one doesn’t have anything (just red), so there is no way of knowing how “positive” the charge is.
More logically is assuming R is the charge distribution i.f.o. theta (R from rho maybe?)
For the monopole moment you would simply integrate over space. But it seems logically (given the theta dependancy) we are not working in a carthesian coordinate system. Therefore we should include a Jacobian determinate. Except we don’t know if we are working in a cylindrical or a spherical system? Which is important as the second one has a cos(theta) in the Jacobian? Or maybe I am searching too far.