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Find the volume of the solid generated by revolving each region about the $y$-axis.The region in the first quadrant bounded on the left by the circle $x^{2}+y^{2}=3,$ on the right by the line $x=\sqrt{3},$ and above by the line $y=\sqrt{3}$
$\sqrt{3} \pi$
Calculus 2 / BC
Chapter 6
Applications of Definite Integrals
Section 1
Volumes Using Cross-Sections
Applications of Integration
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So why? And we could draw on that solar picture to sew a of why it's going to be the outer radius. It's going to be pi times the outer radius squared, which is square three squared three and then minus the inter radius squared, which is the inter radius, is the square root of three minus y squared. So then this squared is just going to be three months y squared. Um, so that is just pi times y squared. And then we're just going to integrate it from zero to the square root of three. You see, so the integral from zero to the square root of three of pi y squared, it's just going to be a pie. Times square root three cubed over three Just going to be the squared of three times pi
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