Also, the Earth's shadow has only approximately the width of $$2r$$. It would have very nearly a width of $$2r$$ if the Sun were a point-like light source (exactly that width if it were infinitely far away). Actually, however, the Sun is large enough to appear as a disk which covers about half a degree of the sky. As a result, the Earth's shadow is not a cylinder but a gradually narrowing cone, and at the Moon's distance it is already about 25% narrower than $$2r$$.