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Flux & Divergence Theorem

Suppose F is a vector field with div F = 10. Find the flush F out of a cylinder of height a and radius a, centered on z-axis and with base in the xy-plane.

By the divergence theorem:

  /                       /
 | div(F) dV = 10 | dV  = 10 * (volume of cone radius a & height a)
 /W                    /W

First, is this part right?
Second, Is there a way to calculate the flux however without knowing the volume of a cone with radius a and height a?


Thanks.
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BrianGEFF719
Asked:
BrianGEFF719
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1 Solution
 
BrianGEFF719Author Commented:
so the answer would be (10 * a^3 *pi)/3
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ozoCommented:
Do you mean cone or cylinder?
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ozoCommented:
Can you integrate to find the volume?
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ozoCommented:
You can integrate the area of circular slices d height, but after you do so you will know the volume of a cone with radius a and height a
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BrianGEFF719Author Commented:
So there is no way around working with the volume of the cylinder?
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ozoCommented:
or cone, whichever.
you don't need to start knowing the volume, but after you find the flux, you will know the volume by the divergence theorem
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