. A silo (base not included) is to be constructed in the form of a cylinder surmounted by a hemisphere. The cost of construction per square unit of surface is twice as great for the hemisphere as it is for the cylindrical sidewall. Determine the radius to be used if the volume is to be 1000 m3 and the cost minimized.

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It's my method of solving this type of account, i get the denominators and multiply them by the fractions, then you cut the denominators, any questions just ask, i don't think that it was clarifying:

(2x-1) . (1-4x^2) . (5/2x-1) + (2x-1) . (1-4x^2) . (6x/1-4x^2) =
-> (1-4x^2) . 5 + (2x-1) . 6x =
-> 5 - 20x^2 + 12x^2 - 6x =
-> -8x^2 - 6x + 5 = 0

Delta = (-6)^2 - 4.(-8).5
Delta = 36 + 160 = 196

x' = - (-6) + sqroot(196) / 2.(-8)
x' = 6 + 16 / -16
x' = 22/-16 (simplifying by 2) = -11/8

x'' = 6 - 16 / -16 = -10/-16 (simplifying by 2)
x'' = 5/8