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The region in the plane bounded by and the -axis for is rotated about the -axis. The
volume of the resulting solid of revolution is (Hints won’t be revealed until after you
choose a response.)
If is used as the slicing variable, then slices are vertical and
consequently perpendicular to the axis of rotation.
Furthermore one side
of the region lies along the axis, so the disk method is appropriate in this
The distance from the axis to the upper edge of the region is , so
The region in the plane bounded on the right by the curve , on the left by the curve ,
and on the bottom by is revolved around the -axis. Compute the volume of the
Compute the volume of the solid of revolution obtained by rotating the region
between , , and around the -axis.
The region between the graph of and the -axis is rotated around the line . What is
the volume of the resulting solid?
Find the volume obtained by rotating the region between the graph and the -axis for
about the -axis.
Sample Exam Questions
Calculate the volume of the solid obtained by rotating the area between the graphs of
and the -axis for around the -axis.
Let be a continuous function that satisfies and for . For every , when the region
between the graph of , the -axis, and the line is rotated around the -axis, the volume
of the resulting solid is . What is ? (Hints will not be revealed until after you choose
By the disk method, we have that for each . Solve this equation for .
both sides with respect to ; use the Fundamental Theorem of Calculus to differentiate
the left-hand side.
Find the volume of the solid generated by revolving the region bounded above by
and bounded below by for about the -axis.