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Math Help - Volume

  1. #1
    tmd
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    Volume

    The base of a solid is the region in the first quadrant bounded by the line x+2y=4 and the coordinate axes. What is the volume of the solid if every cross section perpendicular to the x-axis is a semicircle? (п = pie)
    A. 64п/3
    B. 32п/3
    C. 8п/3
    D. 4п/3
    E. 2п/3

    thanks!
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  2. #2
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    Quote Originally Posted by tmd View Post
    The base of a solid is the region in the first quadrant bounded by the line x+2y=4 and the coordinate axes. What is the volume of the solid if every cross section perpendicular to the x-axis is a semicircle? (п = pie)
    A. 64п/3
    B. 32п/3
    C. 8п/3
    D. 4п/3
    E. 2п/3

    thanks!
    Hello, tmd,

    the semi-circles end at the x-axis and the line y = -1/2x + 2 with y as the diameter of the semi-circles.

    Therefore the radius is r = 1/2*y = -1/4x + 1

    The volume of the solid is:

    V = int from{0} to {4} (pi/2*(-1/4x+1))dx = pi/2*int from{0} to{4} (1/16x - 1/2x + x)dx = pi/2*[1/48x - 1/4x + x]from{0} to{4} = pi/2 * 4/3 = (2pi)/3

    So it's answer E

    EB
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