A silo (based not included) is to be constructed in the form of a cylinder surmounted by hemisphere. The cost of construction per square unit of surface area is 5 times as great for the hemisphere as it is for the cylindrical sidewall. Determine the dimensions to be used if the volume is fixed at 1200 cubic units and the cost of construction is to be kept to a minimum. Neglect the thickness of the silo and waste in construction.
The radius of the cylindrical base (and of the hemisphere) is __ ft. ???

Question

A silo (based not included) is to be constructed in the form of a cylinder surmounted by hemisphere. The cost of construction per square unit of surface area is 5 times as great for the hemisphere as it is for the cylindrical sidewall. Determine the dimensions to be used if the volume is fixed at 1200 cubic units and the cost of construction is to be kept to a minimum. Neglect the thickness of the silo and waste in construction.
The radius of the cylindrical base (and of the hemisphere) is __ ft. ???

anonymous · Answer

$$A=A _{H}+A _{C} = 2\pi r ^{2}+2pih$$

anonymous · Answer

Please confirm one or two hemisphere.

anonymous · Answer

ok this is how far i get $$C=(5)2pir ^{2}+2pirh$$
[12000=2/3 \pi r ^{3}+\pi r ^{2}h\]
$$h= 12000/ \pi r ^{2}- 2r/3$$

anonymous · Answer

Would this be correct??

anonymous · Answer

You need to tell me the hemisphere on one end or on both ends?

anonymous · Answer

What do you mean? i am not understanding

anonymous · Answer

Is that not what i am looking for? for one of the sides of radius or height?

anonymous · Answer

The is an optimization problem. We need to know exactly what the silo looks like. Since the problem said the cylinder surrounded by the hemisphere (singular = one hemisphere) implying the silo has a round to and FLAT bottom. Please verify that I'm correct. I then will explain how to solve the problem.

anonymous · Answer

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