Really need your help guys. I don't even know where to get started. No body can answer this questions so i thought i'd ask the online community :)A silo (base not included) is to be constructed in the form of a cylinder surmountedby a hemisphere. The cost of construction per square unit surface area is twice as great for the hemisphere as it is for the cylindrical sidewall. Determine the dimensions tobe use if the volume is fixed and the cost of construction is to be kept to a minimum.
Volume = πr?h h = Volume/(πr?) area of top cup A1 = 2πr? area of surface A2 = 2πrh = 2πrVolume/(πr?) = 2 Volume/r total cost is: T = A1 (c) + A2 (2c) = 2πr? (c) + (2 Volume/r) (2c) dT/dr = 4πr (c) - (4 Volume/r?) (c) minimum cost if dT/dr = 0 4πr (c) - (4 Volume/r?) (c) = 0 r = ?(Volume/π)
