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Math Help - volume of solids of revolution

  1. #1
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    Exclamation volume of solids of revolution

    hi, i'm doing a maths assignment on "volume of solids of revolution" and stuck on one particular question. the question asks for the volume of the cross bounded by y=x, y=-x, y=x+2, y=-x+2 and the curve y=x^2-4. it is to be rotated around the y-axis. i really don't know how to do it, neither do my classmates. i had an idea of finding the area of the cross and rotating that but it wouldn't work out.
    any ideas?
    thanks in advanced.

    here is a screenshot of the graph.
    Attached Thumbnails Attached Thumbnails volume of solids of revolution-untitled.jpg  
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  2. #2
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    Didn't I already do this one?

    1) Make up your mind about the problem statement.
    2) Axis of rotation is what?
    3) Find the 12 intersections.
    4) etc. What did I say before. I don't recall.
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  3. #3
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    yea you did, but i have figured it out now. i found the 12 intersections and am rotating around the y-axis. thanks for your help
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  4. #4
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    Did you get twice the required answer? It is a common error.
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  5. #5
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    not sure as it is a school assignment, but the answer i got is 48.116units^3. looks about right to me.
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  6. #6
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    I didn't look at it real closely, but I'm closer to \frac{68}{3} \pi, quite a bit more than you managed. I hardly can wait to see your solution.
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  7. #7
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    Heres how I went about it:

    Just consider one side. You can look at it as two branches. The top branch is still bounded by 3 lines. However, if we cut this area in half aloing the the intersection on the middle/outside, then each side is only two lines bouding the areas. If you follow the same pricinple for the bottomw branch, you will have 4 different areas rotated. The is one little bit of overlap, the triangle shape, but you can easily rotate that and subtract it from the total.
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