Question

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 10,800ð ft3.

h=
let's assume that the silo will be totally filled including the hemisphere.
radius of cylinder and hemisphere is 15
let the height up to the hemisphere be h ft

πr^2 h + (1/2) (4/3)πr^3 = volume
π(15)^2 h + (2/3)π (15)^3 = 10800
225πh + 2250π = 10800
h = (10800 - 2250π)/(225π)
= appr 5.28 ft

very strange looking silo
I suspect there is a typo in 10,800ð ft3
Make the necessary correction and repeat the above steps

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