Posted by Anonymous on Wednesday, December 19, 2012 at 6:50am.
A building is in the form of a cylinder surmounted by a hemispherical vaylted dome and contains 1144/21 m3 of air. If the internal diameter of the dome is equal to 4/5th of the total height above the floor, find the height of the building

maths  Steve, Wednesday, December 19, 2012 at 10:57am
v = 2/3 pi r^3 + pi r^2 h
d = 4/5 h, so r = 2h/5
but that's the total height. So, in terms of wall height, r = 2h/3
= pi r^2 (2r/3 + h)
1144/21 = pi (2h/3)^2 (2/3 * 2h/3 + h) = 52pi/81 h^3
h = 3 m
so, the wall is 3m high, and the dome is another 2m high, making the whole structure 5m high.
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