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 903211: 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 13,725π ft3.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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 13,725π ft3.
:
From the information given, we know the radius of the silo = 15 ft
let h = the height of the cylinder portion of the silo (w/o the hemisphere)
:
The total volume equation
pi%2A15%5E2%2Ah + 2%2F3pi%2A15%5E3 = 13725%2Api
simplify, divide equation by pi
15%5E2%2Ah + 2%2F315%5E3 = 13725
Factor out 15^2
15%5E2%28h+%2B+2%2F3+%2A+15%29 = 13725
divide both side by 15^2
h + 10 = 13725%2F15%5E2
h + 10 = 61
h = 51 ft is the height of the cylinder portion of the silo
Add the height of the hemisphere
51 + 15 = 66 ft is the height of the silo