Is My Disk Method Calculation Correct for Finding Volume?

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The discussion focuses on calculating the volume of a solid generated by revolving a shaded region around the y-axis using the disk method. The formula applied is V = ∫ from a to b (π * R(x)² dy), with the specific calculation yielding V = 6π. There was initial confusion regarding the axis of rotation, which was clarified to be the y-axis. The final answer of 6π is confirmed as correct for the volume. The importance of specifying the axis of rotation in such problems is emphasized.
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Homework Statement


Find the volume of the solid generated by revolving the shaded region about the given axis.
61prob14.jpg


Homework Equations


I used the disk method to solve this
V = int from a to b(pi * R(x)^2)


The Attempt at a Solution



V = int from 0 to 2( pi * (3Y/2)^2 dy) = 6pi
 
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TheTaoOfBill said:
Find the volume of the solid generated by revolving the shaded region about the given axis.
Which axis? It's not given.
 
Mark44 said:
Which axis? It's not given.

sorry... Over the Y axis.
 
The region is rotated around (or about) the y-axis. Yes, that's the right answer.
 

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