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Use polar coordinates to find the volume solid under the paraboloid z = x2 + y2 and above the disk x2 + y2 9 40.5 pi -7.5 pi 68.5 pi 140.5 pi -43.5 pi solid bounded by the paraboloid z = 7 - 6x2 - 6y2 and the plane z = 1. 13 pi 6 pi 4.5 pi 2 pi 3 pi solid under the paraboloid z = x2 + y2 and above the disk x2 + y2 49.

MATH 2004 Homework Solution Han-Bom Moon 15.3.36Find the volume of the solid by subtracting two volumes, where the solid is enclosed by the parabolic cylinder y = x2 and the planes z = 3y, z = 2+y. Two planes meet over 3y = 2+y ,y = 1.

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Find the volume of the region bounded above by the paraboloid z = 8-x 2-y 2, bounded below by the paraboloid z = x 2 + y 2, and with y ≥ 0. In cylindrical coordinates, the upper paraboloid becomes z = 8-r 2, and the lower paraboloid becomes z = r 2. These intersect when 8-r 2 = r 2, which we solve to find r 2 = 4.

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How to solve: 1. Find the volume of the region E bounded by the paraboloids z = x^2 + y^2 and z = 36 - 8 x^2 - 8 y^2. 2. Find the centroid of E...

4. Find the volume of the solid lying under the circular paraboloid z= x 2+ y and above the rectangle R= [ 2;2] [ 3;3]. Z 2 3 Z 2 2 x2 + y2 dxdy= Z 3 3 1 3 x3 + y2x x=2 x= 2 dy = Z 3 3 8 3 + 2y2 (8 3 2y2)dy = Z 3 3 16 3 + 4y2 dy= 16 3 y+ 4 3 y3 3 3 = 16 + 36 ( 16 36) = 104 5. Find the volume of the solid under the paraboloid z= 3x 2+y and above ...