There is an imaginary cylinder of base A and slant height ct, where c is the molecular speed and t, a small interval of time. Θ is the angle between the axis of the cylinder and a perpendicular from the wall. And Φ is the angle on the surface of the wall. Molecules in it are moving parallel to the axis, and hence have a perpendicular component to the wall c cosΘ. So, the momentum imparted on the wall by one such molecule will be 2mc cosΘ (where m is the mass of the molecule).

The number of molecules that move parallel to the axis = (Act cosΘ) × (N/V) × (dΦ sinΘ dΘ/4π) [where N is the total number of molecules and V is the total volume, and π is pi though it does not quite look like it].

(dΦ sinΘ dΘ/4π) is found by dividing (r

^{2}sinΘ dΘ dΦ) by the total surface area of the sphere (4πr

^{2}). This is what I did not understand, how did they obtain (r

^{2}sinΘ dΘ dΦ)?

Thank you