WEBVTT
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All right, we want to take the curves,
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Y equals root X and rotate it um around the
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X axis. Let me try rather one more time
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. See if I can draw better. Okay,
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that's a little bit better. So what's happening is
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it's going to come out of the page and then
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back into the page and you're going to get this
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nice um Carrabba, Lloyd looking thing. Okay,
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so what happens? Uh let's first ask ourselves if
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that equation is still valid. Um So now we
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have X. Y and then Z is actually coming
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out of the page. So this is a funny
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looking um three dimensional axis, we normally wouldn't drop
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like this um at every point on that circle is
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why still the root of X will definitely not,
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it's only that on the extremities. So okay,
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so we scrap that equation. That's annoying. We
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don't have anything anymore. So what do we have
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? Well, for each value of X, we
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have something like that red circle and that red circle
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has radius, route X and uh let's see uh
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the circle um so the X stays the same and
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y and Z both change right as we walk around
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that red thing. So um the circle is actually
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uh export dependent on y and Z. So we're
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going to get y squared plus Z squared and then
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it's going to equal the radius squared. Well,
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radius is route X. So you get root X
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squared. So um now the equation for the surface
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is y squared plus Z squared equals X. Um
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So this is a great problem is a lot of
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thinking. Um There's no like formulaic way to solve
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a problem like this, you've got to think about
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what's happening in three dimensions.