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A cylindrical container is to be constructed so that the sum of its height and its diameter is 15 feet.
a) Write an equation relating the height of the cylinder, h, to its radius, r. Solve the equation for h in terms of r.
b) The volume of a cylinder is given V=πr^2h. Use your answer in part A to express the volume of the cylindrical container in terms of r alone. Leave your expression in factored form so that it will be easier to analyze.
c) What are the values of r for which this problem makes sense? Explain.

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