Find the Volume of the Solid Generated by Revolving the Region

question 33

Multiple Choice

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the $x \text {-axis. }$ -axis. Verify your results using the integration capabilities of a Graphing utility.
$y = \sin ( x ) , y = 0 , x = 0 , x = \frac { \pi } { 3 }$

• A) \(\frac { 1 } { 3 } \pi ^ { 2 } - \frac { \sqrt { 3 } } { 8 } \pi\)
• B)\(\frac { 1 } { 6 } \pi ^ { 2 } + \frac { \sqrt { 3 } } { 8 } \pi\)
• C)\(\frac { 1 } { 6 } \pi ^ { 2 } - \frac { \sqrt { 3 } } { 8 } \pi\)
• D)\(\frac { 1 } { 3 } \pi ^ { 2 } + \frac { \sqrt { 3 } } { 8 } \pi\)
• E)\(\frac { 1 } { 6 } \pi ^ { 2 } - \frac { \sqrt { 3 } } { 4 } \pi\)

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