Find the Volume of the Solid Generated by Revolving the Region

question 82

Short Answer

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations and inequalities about the $y$ -axis.
$$x ^ { 2 } - y ^ { 2 } = 81 , x \geq 0 , y = - 9 , y = 9$$

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Definitions:

Circular Runout

A form of measurement that checks the roundness and concentricity of a cylindrical object's surface as it rotates.

Circularity

The condition where all points on a circle’s circumference are equidistant from the center, measuring roundness.

Datum Axis

Datum Axis refers to an imaginary line, plane, or point referenced in manufacturing and design to measure the geometry of parts and assemblies for precise construction.

Total Runout

The comprehensive deviation of a surface from its true rotational path, measured along and around the surface.