A cone has its tip at the point (0, 0, 8) and its base the disk D, x^2 + y^2 les

Question

A cone has its tip at the point (0, 0, 8) and its base the disk D, x^2 + y^2 lessthanorequalto 4, in the xy-plane. The surface of the cone is the curved and slanted face, S, oriented upward, and the flat base, D, oriented downward. The flux of the constant vector field F = ai + bj + ck through S given by integral_s F middot dA = 5.23. What is integral_D F middot dA? integral_D F middot dA = (Enter indeterminate if it is not possible to find a value given the information provided.) Supposed we instead consider the vector field F = ai + bj + czk. If we again know integral_S F middot dA = 5.23. What is integral_D F middot dA in this case? integral_D F middot dA = (Again, enter indeterminate if it is not possible to find a value given the information provided.)

Explanation / Answer

Since D is in XY-plane, z=0

Thus flux over D becomes -5.23

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