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

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Question 1203360: A large grain silo is to be constructed in the shape of a circular cylinder with a hemisphere attached to the top (see the figure). 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 ft^3
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39615) About Me  (Show Source):
Answer by greenestamps(13198) About Me  (Show Source):
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The radius of the cylinder and hemisphere is 15 ft.

The volume of the hemisphere is

%282%2F3%29%28pi%29%2815%5E3%29=2250+pi

So the volume of the cylinder is

11925pi-2250pi=9675pi

%28pi%29%28r%5E2%29%28h%29=%28pi%29%28225%29%28h%29=9675pi
h=9675%2F225=43

The height of the cylinder is 43 feet.

ANSWER: The height of the silo is 43+15 = 58 feet