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Cylinder Problems 1. An 8 1/2 x 11 piece of paper can be formed into a cylinder in two different ways - “tall” or “short.” Without any calculations, which way, if any, has the greater volume? And lateral area? Put only two √ on the chart. tall short same LA Vol Verify your prediction by determining the lateral area and volume of each cylinder. tall LA Vol short same 2. A right cylinder has a volume of 16π cubic units. To find the minimum possible surface area, solve the equation for volume for h: V = πr2h Since V = 16π substitute that in the new equation and then in the equation for surface area. Using a graphing calculator put the surface area equation in the y= with 0 < x < 10 and 0 < y < 200. Find the minimum surface area. What is the height of that cylinder? What is that surface area? 3. You have been asked to design a one liter oil can shaped like a right cylinder. What dimensions will use the least amount of material? 4. A processing plant is designing a can that can hold 64 fl oz. or 115.5 in3 and uses the least amount of material. Find the minimum surface area. 5. A processing plant is designing a can that can hold 60 in3 and uses the least amount of material. Find the minimum surface area. 6. A processing plant is designing a can that can hold 18 cu. yds. and uses the least amount of material. Find the minimum surface area.