# SOLUTION: A can in the shape of a right circular cylinder is required to have a volume of 700 cubic centimeters. The top and bottom are made up of a material that costs 8¢ per square centime

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 Question 350885: A can in the shape of a right circular cylinder is required to have a volume of 700 cubic centimeters. The top and bottom are made up of a material that costs 8¢ per square centimeter, while the sides are made of material that costs 5¢ per square centimeter. Find a function that describes the total cost of the material as a function of the radius r of the cylinderAnswer by nerdybill(6958)   (Show Source): You can put this solution on YOUR website!A can in the shape of a right circular cylinder is required to have a volume of 700 cubic centimeters. The top and bottom are made up of a material that costs 8¢ per square centimeter, while the sides are made of material that costs 5¢ per square centimeter. Find a function that describes the total cost of the material as a function of the radius r of the cylinder . Volume is "area of bottom" times "height" giving us (let h = height): (3.14r^2)h = 700 Solving for h: height = 700/(3.14r^2) . Area of side: circumference * height circumference is (pi)d or (pi)(2r) or (3.14)(2)r or 6.28r "area of side" = 6.28r * 700/(3.14r^2) = 1400/r . Area of top and bottom: (pi)r^2 = 3.14r^2 . Cost = "top" + "bottom" + "side" . C(x) = .08(3.14r^2) + .08(3.14r^2) + .05(1400/r) C(x) = 2(.08(3.14r^2)) + .05(1400/r) C(x) = .5024r^2 + 70/r (this is what they're looking for) where C(x) is the cost