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A right circular cone has a semi-vertical angle
. Calculate the solid angle at the apex P of the cone. |
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The cap on the cone is a part of a sphere of radius R, the slant length of the cone. Using spherical polar coordinates, an area element on the cap is
sin
,
where is
the polar angle and is the azimuthal angle. Here, goes from 0 to
while goes from 0 to . |
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Thus the area of the cap is |
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Thus the solid angle at P is |