Use polar coordinates to find the volume of the given solid. bounded by the paraboloid z = 9 + 2x2 + 2y2 and the plane z = 15 in the first octant

Z = 8 + 2x2 + 2y2

Convert to polar coordinates

Z = 8 + 2r2

Now theta will go from 0 to pi/2 because it's in the first quadrant.

R will go from 0 to the radius of the circle formed at the intersection of the plane and the paraboloid.

14 = 8 + 2r2

r = sqrt(3)

So r goes from 0 to sqrt(3).

You integrate 14-z where 0<r<sqrt(3) and 0<theta<pi/2.

It is 14-z and not z because just z would give the volume under the paraboloid.

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the answer

b. they are parallel and will never intersect.

a. she will receive a refund of $278.

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