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March 27, 2017

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Let R be the region bounded by the x-axis, x = 5 and the curve
y = x. This region is rotated around the x-axis. Find the volume of the resulting
solid. (Note: R is a triangular region. The resulting solid has a simple shape.
You may ask me if you are highly unsure about what the solid "looks like.")

  • Calculus - ,

    geometrically, the solid is a cone of height=5, radius=5

    v = 125/3 pi

    Analytically,

    v = Integral(pi * y^2 dx)[0,5]
    = Integral(pi * x^2 dx)[0,5]
    = pi/3 x^3 [0,5]
    = 125/3 pi

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