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Ksju [112]
2 years ago
11

Use polar coordinates to find the volume of the given solid. Bounded by the paraboloid z = 6 + 2x2 + 2y2 and the plane z = 12 in

the first octant
Mathematics
1 answer:
ololo11 [35]2 years ago
6 0

Answer:

\frac{9\pi }{4}

Step-by-step explanation:

Paraboloid z = 6 + 2x^2 + 2y^2 ----- ( 1 )

plane z = 12

equation 1 becomes

12 = 6 + 2( x^2 + y^2 )

hence : ( x^2 + y^2 )  = 3

This shows that the solid lies under the parabolic and above the disk  0 : x^2 + y^2 ≤ 3

attached below is the remaining part of the solution

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