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    Question 2

    Number and Inequalities

    1.A cylindrical vessel with one end open is made from a given piece of material. Show that its volume is greatest if the height and radius are equal.

    2. a,b,c are non zero rational numbers. Show that if:

    ³√a + ³√b + ³√c = 0

    And if none of ³√a , ³√b , ³√c is rational then ³√a , ³√b , ³√c are rational multiples of the same irrational number.

    © BrainMass Inc. brainmass.com March 4, 2021, 11:28 pm ad1c9bdddf
    https://brainmass.com/math/basic-algebra/number-inequalities-425753

    Solution Preview

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    Question 2

    Number and Inequalities

    1.A cylindrical vessel with one end open is made from a given piece of material. Show that its volume is greatest if the height and radius are equal.

    As the cylinder is made from a given piece of material, the surface area of the cylinder remains constant. Let the surface area of the cylinder is A, and is constant.
    Let the cylinder has the radius r and height h.
    As the cylinder is open at one end, the total surface area is given by A = (pie)r^2 + 2(pie)rh...(1)
    Solving this for 'h' we get:
    h = A - (pie)r^2/2(pie)r...(2)
    We know that the volume of the cylinder is given by V = (pie)r^2 h...(3)
    Using the equation (2), we can write equation (3) as
    (please see the attached file)

    Differentiating with respect to r., we ...

    Solution Summary

    This solution presents rational multiples of the same irrational number.

    $2.49

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