A building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contains 411921m3 of air. If the internal diameter of dome is equal to its total height above the floor, find the height of the building?
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Let total height of the building = internal diameter of the dome = 2 r m
∴Radius of building ( or dome) = 2r2=rm
Height of cylinder = 2r – r = r m ∴ Volume of the hemispherical dome cylinder = 23πr3m3 ∴Total volume of the building = Volume of the cylinder + Volume of hemispherical dome =(πr3+23πr3)m3=53πr3m3
According to the question, Volume of the building = volume of the air ⇒53πr3=411921⇒53πr3=88021⇒r3=880×7×321×22×5=40×2121×5=8m3 ⇒r=2m ∴ Height of the building = 2r=2×2=4m