A propane tank is to hold a volume of 380 m of propane. The tank will...

 

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A propane tank is to hold a volume of 380 m of propane. The tank will be in the shape of a cylinder with a hemisphere on one end. The machinery cannot manufacture a cylinder with any measure (including the radius) that is any smaller than 2 m. The cost of the surface area for the hemisphere is 8/3 times that of the cylinder (8:3 ratio respectively). The radius that will minimize the overall cost (to two 2 decimal places) is: A propane tank is to hold a volume of 380 m of propane. The tank will be in the shape of a cylinder with a hemisphere on one end. The machinery cannot manufacture a cylinder with any measure (including the radius) that is any smaller than 2 m. The cost of the surface area for the hemisphere is 8/3 times that of the cylinder (8:3 ratio respectively). The radius that will minimize the overall cost (to two 2 decimal places) is:

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Lets denote the radius of the cylinder as r and the height of the cylinder as h S... View the full answer