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Simple geometrical problem

  1. Apr 20, 2008 #1
    Does anyone can help me how to find [tex]r * sin \theta * d\phi[/tex] (please see attached image)?

    Here some other that I can solve:

    FIRST

    [tex]d\theta = L / r[/tex]

    so

    [tex]L = r * d\theta[/tex]

    SECOND

    [tex]sin \theta = P / r[/tex]

    so

    [tex]P = r * sin \theta[/tex]

    THIRD

    [tex]d\phi = B / r[/tex]

    so

    [tex]B = r * d\phi[/tex]

    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:

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

    Also, how to obtain [tex]d\omega = dS / r^2[/tex]?

    Thanks in advance
     

    Attached Files:

  2. jcsd
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