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A building is in the form of a cylinder surrounded by a hemispherical vaulted dome and contains 41(19/21-) cu m of air. If the internal diameter of the building is equal to its total height above the floor, find the height of the building.
( Ans : 4m)
Ans: Volume of building = 41 (19/21) m^{3}
=> π.r^{2}.r + 2/3 π r^{3} = 41(19/21)
=> π × r^{3} × 5/3 = 880/21
=> r ^{3} = 880/21 x 7/22 x 3/5
=> r^{3} = 8
=> r = 2 m
∴ height of building = 4 cm
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