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If you have only 500 sq. feet of material and have to built a swimming pool, which shape will hold the most water. A cylinder, a cube or a rectangular prisim?

  • Geometry -

    Is the material used for the liner of the pool?
    Is this a question from a Calculus course?

    Let the base be a square, (again an assumption)
    let the base by x by x feet, let the height be y feet
    then x^2 + 4xy = 500
    4xy = 500- x^2
    y = (500 - x^2)/(4x)

    volume = x^2y
    = x^2(500 - x^2)/(4x)
    = 500x^2 = x^3/4

    differentiate and set that equal to zero and solve.
    You will get a quadratic equation with two roots.
    Discard the negative root if there is one.

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