Pregunta
Show all your work to receive full credit. Write your answers as complete sentences.
- Use the method of cylindrical shells to find the volume of the solid of revolution generated
by rotating the region between the graphs of
, and
about the
-axis.
by rotating the region between the graphs of
Ask by Thornton Powell. in the United States
Jan 23,2025
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Respuesta verificada por el tutor
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The volume of the solid is
cubic units, which is approximately
cubic units.
Solución

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To find the volume of the solid of revolution generated by rotating the region bound by the graphs of
,
,
, and
about the
-axis using the method of cylindrical shells, we start with the formula:
Here,
represents the height of the shell, which is
, and
and
.
Substituting our variables into the volume formula, we have:
Now, we compute the integral:
Evaluating the definite integral from 1 to 10 gives us:
Now substituting back into our volume equation:
Thus, the volume of the solid of revolution generated by rotating the region about the
-axis is:
This expression represents the volume, providing the complete answer as requested.

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