Manufacturing cylindrical vents: JA = 2mrh lv mr?h %3! In the manufacture of cylindrical vents, a rectangular piece of sheet metal is rolled, riveted, and sealed to form the vent. The radius and height required to form a vent with a specified volume, using a piece of sheet metal with a given area, can be found by solving the system shown. Use the system to find the radius and height if the volume required is 4071 cm3 and the area of the rectangular piece is 2714 cm2.