Question: Use the divergence theorem, assuming that the assumptions on T and S are satisfied. Show that a region T with boundary surface S has the

Use the divergence theorem, assuming that the assumptions on T and S are satisfied.

Show that a region T with boundary surface S has the volume

-Hгc V = r cos ф dA

where r is the distance of a variable point P: (x, y, z) on S from the origin O and Ï• is the angle between the directed line OP and the outer normal of S at P.

Make a sketch. Use (2) in Sec. 10.7 with F = [x, y, z].

-Hc V = r cos dA

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