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The base of a solid is a region bounded by the curve (x^2/8^2)+(y^2/4^2)=1 (an ellipse with the major and minor axes of lengths 16 and 8 respectively). Find the volume of the solid if every cross section by a plane perpendicular to the major axis (x-axis) has the shape of an isosceles triangle with height equal to 1/4 the length of the base.

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2 answers

  1. This is just like the other one The base of each triangle has length 2x,
    making the area 1/2 bh = 1/2 (2x)(x/2) = 1/2 x^2
    Using the symmetry of the figure,
    v = 2∫[0,8] 1/2 x^2 dx

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  2. same oops as before.
    v = 2∫[0,8] 1/2 y^2 dx = v = 2∫[0,8] 1/2 (16 - x^2/4) dx

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