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Calculate a volume using the washer method

  1. Jun 29, 2009 #1
    1. The problem statement, all variables and given/known data

    y=x^2+1
    y=9-x^2
    y=-1 rotate

    2. Relevant equations



    3. The attempt at a solution

    intersection
    x^2+1=9-x^2=>2x^2-8=0=>2(x^2-4)=0=>x=+-2
    Washer method
    outer radius = 1+9-x^2=10-x^2
    inner radius = 1+x^2+1=2+x^2
    Area=pi((10-x^2)^2-(2+x^2)^2)=pi(100-20x^2+x^4-4-4x^2-x^4)=pi(96-24x^2)=24pi(4-x^2)
    by symatrey
    V=48pi Integral( 4-x^2,x,0,2)=48pi[4x-x^3/3,0,2]=48pi(8-8/3)=48pi(24-8)/3=48pi*16/3=256pi

    if you can try and solve to verify please, or else if you have a membership to cramster this is problem 10 in the the chapter 6 review stewart 5e
     
  2. jcsd
  3. Jun 29, 2009 #2

    zcd

    User Avatar

    Re: volumes

    Yes, 256pi is right. You could always try the problem by both shell and washer method to check the answer.
     
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