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
