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Numerade Educator

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Problem 20 Easy Difficulty

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

$ \Re_1 $ about $ OC $

Answer

$\frac{2 \pi}{3}$

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Video Transcript

you we're giving a figure which contains a region in the line. And we have to find the volume of the generated by rotating this region about this line. It's just all The region is the region are one about the line. Oh see and this is in the figure and exercise 20 of this section, crush it. Mhm. At my wins. So notice that by rotating this region around Oc we're rotating around the Y axis. She uh Jason jake. Let's talk about your black experiences. It's great. I don't know what everyone's complaining about. There we go. That's what we're lucky. The and therefore we're going to use the washer method. Never. Yeah. No, I just just follow the rules and you don't get arrested. It's been arrested. Like now try me out earning a radius. You see that from the figure our our radius Is x equals 1 0, which is just one course. And the inner radius. Yeah, well this is going to be released. There's a cop just Yeah, X equals Y. I just did the thing I was like that will never happen -6 equals one. I started getting more violent. Sorry minus zero is equal to Y. And so the volume by the washer method life I remember like the so he is pi times in the growth from or you know white blue or why equals zero of the Y equals one of the outer radius one squared most inner radius Y squared Dy. And if you evaluate this simple integral, the answer is two pi over three car. Yeah that didn't exist. You have noticed.