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The base of a certain solid is the triangle with vertices at (-14,7),(7,7) and the origin. Cross-sections perpendicular to the y-axis are squares. What is the volume of this solid?

  • Calculus -

    Integrating along y, the area of each cross-section is (2x)^2, so

    v = ∫[0,7] (2x)^2 dy
    Now, x = (7-y), so
    v = ∫[0,7] (2(7-y))^2 dy
    = 4* 1/3 (y-7)^3 [0,7]
    = 1372/3

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