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Help with calc

  1. Jan 9, 2005 #1
    The base od a solid is a region in the 1st quadrant bounded by the x-axis, y-axis and the line x+2y=8. If cross sections of the solidperpendicular to the x-axis are semicircles, what is the volume of the solid?

    How come the answer isnt just the intgegral from 0-8 of 1/2pi(4-x/2)^2
  2. jcsd
  3. Jan 9, 2005 #2


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    That's what it looks like to me. Is it the wrong answer?
  4. Jan 9, 2005 #3
    yea according to the answer key its wrong
  5. Jan 9, 2005 #4
    choices are
    a. 12.566 b. 14.661 c. 16.755 d 67.021 e 134.041

    i keep ending up with choice d but the answer key says its choice c
  6. Jan 9, 2005 #5


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    Oh I see now. I misunderstood the problem. I did it by finding the solid after rotating about the x-axis and integrating... But the cross section of this solid is the circle whose diameter is from y=0 to y=4-x/2. We were thinking the cross section was a circle with diameter from y=-(4-x/2) to y=4-x/2. But if we make the radius (4-x/2)/2, then we get the right answer.

    0-8 of 1/2pi[1/2(4-x/2)]^2 is correct.
  7. Jan 9, 2005 #6
    yea i realized that too thanks
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