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Math Help - Solid of Revolution Answer Check

  1. #1
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    Solid of Revolution Answer Check

    Hi,

    I just wanted to confirm that I got the correct answer for this problem:

    The region bounded by y = x^ 3,x = 2, and y = −1 is revolved about the line y = −8. Find the volume.

    I got the integral from x=-1 to x=2 of pi(x^3+8)^2-81pi

    And my answer is 192pi/7.

    Is this correct?

    Thanks!
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  2. #2
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    Quote Originally Posted by MEnnen View Post
    Hi,

    I just wanted to confirm that I got the correct answer for this problem:

    The region bounded by y = x^ 3,x = 2, and y = −1 is revolved about the line y = −8. Find the volume.

    I got the integral from x=-1 to x=2 of pi(x^3+8)^2-81pi

    And my answer is 192pi/7.

    Is this correct?
    recheck the value of the washer's inner radius. the distance from -1 to -8 is not 9.
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  3. #3
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    Here's a sketch
    Attached Thumbnails Attached Thumbnails Solid of Revolution Answer Check-y-x-3-bounded.jpg  
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  4. #4
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    Ah indeed!

    x=-1 to x=2 of pi(x^3+8)^2-49pi

    864pi/7
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