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Find the volume obtained by rotating the region bounded by y = 0 and y = sqrt(25 - x^2) about the...

Question:

Find the volume obtained by rotating the region bounded by {eq}\; y = 0 \; {/eq} and {eq}\; y = \sqrt{25 - x^2} \; {/eq} about the {eq}y {/eq}-axis.

Volume of Revolution:

1. Find the radius of a differential volume which looks like circular disk when the curve is revolved around the y-axis.

2. Then integrate this differential volume with respect to y.

3. Put the values of the lower and upper limits of y.

Answer and Explanation:

{eq}\; y = \sqrt{25 - x^2} \; {/eq}

Consider a circular disk like cross-section at height y from origin. The radius of this circle is equal to x. If...

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How to Find Volumes of Revolution With Integration

from Math 104: Calculus

Chapter 14 / Lesson 5
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