3.(14 pts) Find an iterated integral whose value equals the volume of the region W above the graph of the paraboloid z = x^2 + y^2 and below the plane z = 9. Then compute the integral. Hint: Use polar or cylindrical coordinates.
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To find the intersection of these surfaces, we set them equal to each other: $x^2 + y^2 = 9$ This equation represents a circle of radius 3 in the $xy$-plane. Therefore, the region W is a solid that looks like a "bowl" with a circular base of radius 3 and a Show more…
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