A wine barrel is designed with interior profile given by rotating the graph of the function f(x) = 1 x² + 2x + 40 for x E [0, 80], where h = 80 is the height of the barrel measured in centimeter and the base of the barrel is at x = 0. (a) What is the diameter of the base of the barrel? What is the diameter of the surface at the top? Show your working. (b) Find the volume of the wine barrel, showing your working. (c) The empty barrel is later converted into a table, where a cut-to-size sheet of glass is put on top of it. What is the surface area of the glass top?

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