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Many kinds of volumes

  1. Apr 6, 2013 #1
    A solid has as its base the region bounded by the curves y=-2x^2=2 and y=-x^2 +1. Find the volume of the solid if every cross section of a plane perpendicular to the x-axis is a trapezoid with lower base in the xy-plane upper base equal to 1/2 the length of the lower base, and height equal to 2 times the length of lower base.

    Lower base: this is the difference between the two functions, or (-2x^2+1) -
    (-x^2+1). Simplify that and you have your lower base.

    Upper base: as given, it's half of the lower base. So once you know the
    lower base, cut it in half and you have your upper base.

    Height: This, too is given in terms of your lower base, so double that lower
    base and now you have your height.

    When you put it together, remember that A = (1/2)(b1+b2)(h). Plug in what
    you found above and have at it!
  2. jcsd
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