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A building is in the form of a right circular cylinder surmounted by a hemispherical dome having the same base radii. The base diameter of the dome is equal to 2/3 of the total height of the building. Find the height if the building, if it contains 1408/21 cubic meter of air.
Let h be the height of cylinder and r be the common base radii of cylinder and hemisphere and H be total height of building.


Diameter of dome = 2r 


6r = 2h + 2r
4r = 2h
?h = 2r
According to given condition,
Volume of air inside the building = Volume of cylinder + Volume of hemisphere



r 3 = 8
? r 3 = (2)3
? r = 2 cm
? h = 2r
      = 2 × 2 = 4 cm
Hence height of building = H = h + r
= 4 + 2 = 6 cm


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