Find the Volume of the Solid Generated by Revolving the Region

question 47

Multiple Choice

Find the volume of the solid generated by revolving the region about the given axis. Use the shell or washer method.
-The region in the first quadrant bounded by $x = 3 y - y ^ { 2 }$ and the $y$ -axis about the $y$ -axis

• A) \(\frac { 81 } { 5 } \pi\)
• B) \(\frac { 243 } { 10 } \pi\)
• C) \(\frac { 243 } { 40 } \pi\)
• D) \(\frac { 81 } { 10 } \pi\)

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