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Math Help - Volume/Pappus' Theorem -- 30 mins remaning

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    Volume/Pappus' Theorem -- 30 mins remaning

    Use Pappus's Theorem to find the volume of the torus obtained when the region inside the circle x^2 + y^2 = a^2 is revolved about the line x = 2a.
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  2. #2
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    Hello, thedoge!

    Do you know Pappus' Theorem? .Did you make a sketch?


    Use Pappus's Theorem to find the volume of the torus obtained
    when the region inside the circle x^2 + y^2 = a^2 is revolved about the line x = 2a

    Pappus' Theorem . . . The volume of a solid of revolution is equal to:
    the area of the region times the distance travled by its center of mass.

    The area of the circle is \pi a^2. .The center of mass is its center.

    The distance travelled is the circumference of a circle with radius 2a\!:\;\;2\pi(2a) = 4\pi a

    Therefore, the volume is: . V \;= \;(\pi a^2)(4\pi a) \;= \;4\pi^2a^3

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