SOLUTION: A large grain silo is to be constructed in the shape of a circular cylinder with a hemisphere attached to the top. The diameter of the silo is to be 30 feet, but the height is yet

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Question 897721: A large grain silo is to be constructed in the shape of a circular cylinder with a hemisphere attached to the top. The diameter of the silo is to be 30 feet, but the height is yet to be determined. Find the height h of the silo that will result in a capacity of 11,925π ft3.
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
The radius is half the diameter, so r=15 feet.

Let h = tallness of only the straight cylinder portion. The whole silo tallness will be highlight_green%28h%2Br%29. Your question is unclear, but you want a final result of either h or h+r.

Volume of the silo, h%2Api%2Ar%5E2%2B%281%2F2%29%284%2F3%29pi%2Ar%5E3=11925pi.
h%2Api%2Ar%5E2%2B%282%2F3%29pi%2Ar%5E3=11925pi
h%2Ar%5E2%2B%282%2F3%29r%5E3=11925
hr%5E2=11925-%282%2F3%29r%5E3
h=11925%2Fr%5E2-%282%2F3%29%28r%5E3%29%2Fr%5E2
h=11925%2F225-%282%2F3%29r
h=11925%2F225-2%2A15%2F3
h=11925%2F225-10=53-10
highlight%28h=43%29 feet, just the straight cylinder part.

The whole silo from top to bottom is 43%2B15=58 feet.