Use polar coordinates to find the volume of the given

Jason Watson

Jason Watson

Answered question

2021-12-04

Use polar coordinates to find the volume of the given solid. Below the paraboloid z=182x22y2 and above the xy-plane

Answer & Explanation

Geraldine Flores

Geraldine Flores

Beginner2021-12-05Added 21 answers

First, find the intersection of paraboloid and xy plane. Setting z=0 we obtain a circle as the intersection:
x2+y2=9
Setting polar coordinates yields the integral:
02π0318r2r3drd0=81π
Result:
81π

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