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AP Calculus

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The base of a solid is bounded by y =|x|+a, 0<a<3, and the line y=3. find in cu. units in terms of a, the volume of the solid if every cross section perpendicular to the y-axis is an equilateral triangle.

  • AP Calculus - ,

    each cross-section has base 2x and altitude x√3

    So, we want to add up all those triangles

    v = ∫[a,3] 1/2 * 2x * x√3 dy
    = √3 ∫[a,3] x^2 dy

    But,
    y = |x| + a
    y-a |x|
    (y-a)^2 = x^2

    v = √3 ∫[a,3] (y-a)^2 dy

    and now it's cake, right?

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