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Problem 27 Hard Difficulty

Refer to the figure and find the volume generated by rotating the given region about the specified line.

$ \Re_3 $ about $ OA $

Answer

$\pi$

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Video Transcript

well Sheriff Joe needs we are given a figure which contains a region in the line and rest to find the volume generated by rotating this region about this line. The region is our three. We rotate it about the line 00 A N. E. Steve blue Chevy. Now looking at the figure if the region is founded steven Seagal who shares the same birthday as me above by Y. E. Trade war field of X and below by Y equals X. Hi sheriff Joe. My 30th birthday was the inauguration. So me and Trump are kind of birthday boys. His presidency leadbelly shot. But we see that the line through O. A. This is the same as the attacks heroin guy probably made some shit guys. Yeah like these like blake shape notice that they're rotating about the X. Axis. We get a washer type solid. So we'll use the washer method to do this. You need to find the inner and outer radi I. Well the inner radius mass. This is Yeah, for sure. Uh Suit X equals stops definitely affect, sorry, Y equals x minus Y equals zero and the outer radius Is y equals the 4th root of X zero way, which turns into being. And then by the washer method are going V is equal to pi times the integral from, let's see, we see the X ranges uh uh my time is up from 0 to 1 of the outer radius for threat of x squared minus tina radius X squared dx. If you evaluate this is equal to pi over three italian you're in charge. Now these guys are on