According to the Stefan-Boltzmann law, the total radiant power $P$ emitted by a star of radius $r$ and temperature $T$ is $P = \sigma A T^4 = \sigma (4\pi r^2) T^4$. This energy spreads uniformly over a spherical region as it travels outwards. At a distance $R$ from the center of the star, the energy crosses a spherical surface of area $4\pi R^2$. Therefore, the radiant energy received per unit area per unit time (intensity $I$) at distance $R$ is given by: $I = \frac{P}{4\pi R^2} = \frac{\sigma (4\pi r^2) T^4}{4\pi R^2} = \frac{\sigma r^2 T^4}{R^2}$.