Let's say I want to model a star of radius $R$ at a distance $r$ from the Earth. I need to show that the apparent luminosity for frequency $\nu$ is equal to
$$\ell(\nu)=\frac{2\pi h}{c^2}\left( \frac{R}{r}\right)^2\frac{\nu^3}{\exp\displaystyle\left(\frac{h\nu}{kT}\right)-1} $$
Which is Planck's law multiplied by $$\pi\left(\frac{R}{r}\right)^2$$
Given the nature of the factor (adimensional function of $R,r$) I would say that the result follows from geometrical considerations, however I fail to see which ones.