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A grain silo consists of a cylindrical concrete tower surmounted by a metal hemispherical dome. The...

A grain silo consists of a cylindrical concrete tower surmounted by a metal hemispherical dome. The metal in the dome costs 1.6 times as much as the concrete​ (per unit of surface​ area). If the volume of the silo is 550 m cubed​, what are the dimensions of the silo​ (radius and height of the cylindrical​ tower) that minimize the cost of the​ materials? Assume the silo has no floor and no flat ceiling under the dome.

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