UCI
MATH 2E -
Quiz 1
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Math 2E 44275 Spring 2014 Quiz 1 4 10 14 Name Print ID Number Show all of your work Partial credit will be given 1 10 points Evaluate ZZZ z dV E where E is enclosed by the paraboloid z x2 y2 and the plane z 3 Solution The paraboloid z x2 y2 r2 intersects the plane z 3 in the circle x2 y2 3 or r2 3 r 3 so in cylindrical coordinates Thus ZZZ z dV E E r z 0 0 r 3 r2 z 3 z r dzdrd 0 3 0 Z 2 Z Z 3 cid 18 9 Z 2 Z 2 r 1 cid 20 9 cid 21 2 r5 4 r2 1 12 r6 r2 3 0 0 3 0 cid 19 2 9 Z 2 Z Z 2 0 0 3 cid 20 1 Z 2 rz2 3 cid 21 z 3 cid 18 9 2 r 1 2 r5 drd z r2 cid 19 dr drd d 0 0
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