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Use the Theorem of Pappus to find the volume of t…

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Problem 44 Hard Difficulty

Use the Theorem of Pappus to find the volume of the given solid.
A sphere of radius $ r $ (Use Example 4.)

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Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 8

Further Applications of Integration

Section 3

Applications to Physics and Engineering

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Video Transcript

in this problem, whereas to use to shape, given an example for and used thermal buckets to coax the William office affair offer. Eighties are all right. This is the shape an example for you know that the example for central adopt This is located as at zero and four are or three pie. Let's assume that now we're rotating this around the necks access. So I actually have a central right that this is our central for a visiting that he would get such a disk. Right now we know that this radius off that desk, let's say, kept our capital R is equal to four are over three pumps, and that's her conference off this desk would be to pie attempts come to our, which is two pi times for our or three pine Prize will cancel out that is eight R or three en de area off a, uh, office original. Similar circle as one house off pi R squared. All right now, terrible focus tells us that volume is ego to be circumference multiplied by the area circumference off this rotated object shaped as eight R or three and area off arc initial southwest circle is one Health pi r Squared and multiplication off Those two is volume which is equal to four over three pi r cubed.

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