Use a triple integral to find the volume of the given solid.The solid enclosed by...

Question

Question

Use a triple integral to find the volume of the given solid.

The solid enclosed by the paraboloids

y = x² + z²

and

y = 72 − x² −z².

Answer 1

Answer #1

In the enclosed solid: the paraboloid: y=72-x2-z2 lies above the paraboloid: y=x2+z2

Hence,

We consider the polar coordinates in xz plane with (r,theta) coordinates

Hence,

Denote area element in xz plane be dA

Hence,

Hence Volume, V=

Answer 2

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