Problem 5.12

A small lamp having the form of a uniformly luminous sphere of radius $R=6.0 \mathrm{~cm}$ is suspended at a height $h=3.0 \mathrm{~m}$ above the floor. The luminance of the lamp is equal to $L=2.0 \cdot 10^{4} \mathrm{~cd} / \mathrm{m}^{2}$ and is independent of direction. Find the illuminance of the floor directly below the lamp.