Simple geometrical problem

1. Apr 20, 2008

Does anyone can help me how to find $$r * sin \theta * d\phi$$ (please see attached image)?

Here some other that I can solve:

FIRST

$$d\theta = L / r$$

so

$$L = r * d\theta$$

SECOND

$$sin \theta = P / r$$

so

$$P = r * sin \theta$$

THIRD

$$d\phi = B / r$$

so

$$B = r * d\phi$$

FOURTH

The pink-hatched region is a regular rectangle with length L and width W.
So the area of this rectangle denoted by dS is:

$$dS = width * length = (r * sin \theta * d\phi) (r * d\theta) = r^2 * sin \theta * d[tex]\theta * d\phi$$

Also, how to obtain $$d\omega = dS / r^2$$?