How to calculate dA of a hemisphere.

[physiker99]

I am not sure about how the integrations are initiated at the question below.

http://img4.imageshack.us/img4/2831/123io.png

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How does dA differ from dV and how are boundaries for integrations are done?

 

[Oerg]

dS is the infinitesimal area element of a sphere in this case. It is given by
$$dS=R^2\sin{\theta}d\theta d\phi$$

Its direction is radial, that's why you have the component $$v_r$$ in the second step.

$$dS$$ can be thought of as 2 parts. The first part is $$R\sin{\theta}d\phi$$, which can be thought of as the base of the rectangular area. The second part is $$R d\theta$$, which is the height of the rectangular area.