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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

Sagot :

batolisis

Answer:

[tex]\frac{9\pi }{4}[/tex]

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

View image batolisis
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