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    Calculus: Area and volume

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    1. A solid is bounded by two bases in the horizontal planes z = h/2 and z = -1/2, and by such a surface that the area of every section in a horizontal plane is given by a formula of the sort

    Area = a0 z3 + a1 z2 + a2 z + a3

    (where as special cases some of the coefficients may be 0). Show that the volume is given by the formula

    V = 1/6?h [B1 +B2 + 4M],

    where B1 and B2 are the areas of the bases, and M is the area of the middle horizontal section. Show that the formulas for the volume of a cone and of a sphere can be included in this formula when a0 = 0

    © BrainMass Inc. brainmass.com March 4, 2021, 6:13 pm ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/calculus-area-volume-35835

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    Solution Summary

    The function of area is given and the volume is calculated.

    $2.49

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