I would like to find the mass of the unit sphere such that the density at any point is proportional to the distance from the surface of the sphere. I think spherical coordinates would probably be best to accomplish this.
I know that $$ mass = \iiint_D\rho(x,y,z) dV $$ but I do not understand how to translate "proportional to the distance from the surface of the sphere" symbolically. I know that the bounds of the integral will be easy to write in spherical coordinates. I need help to understand how to find the density function. I am looking for help to set up the integrand. I can solve the integral myself. Any help would be greatly appreciated.