A grain silo has the shape of a right circular cylinder surmounted by a hemisphere. If a silo is to be constructed to have a capacity of 2000 cubic feet, then what height and radius of the silo will require the least amount of construction material?So far all i have is 2000 = (4*pi*R^3)#92;6 + pi*R^2*Ythen i solve for Y and get (2000-(4piR^3#92;6))#92;piR^2 without simplifying of course, anyway when i substitute Y in the volume equation i get the only possibility is X = 1, but i was under the inpression there should be more than one possibilities because that would make for a 600 some foot tall silo, plus tells nothing of building material unless i compare the findings to the total areas of other combinations.The silos radius must be equal to the cylinders so im not sure. Thanks.
okay, the problem with your substitution, is that it cancels out all variables. The pi*R^2's cancel out, and so do the other variables, leaving you with 2000 = 2000 The important thing to notice is the least amount of construction material. In mathematical terms for this equation, it means the surface area of the general dome + hemisphere shape (disregard support beams or whatnot that would be used in actual construction) For this problem, the surface area of the silo would be 2piR^2 (hemisphere) + 2piR*Y (cylinder) = A use that information and see if you can come up with a better answer. =)
