Q. 154.2( 24 Votes )

# A building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contains of air. If the internal diameter of dome is equal to its total height above the floor, find the height of the building?

Answer :

Let the radius of surmounted hemispherical dome = r

Diameter of hemispherical dome = 2r

Given,

Total height of dome = 2r

Height of hemispherical part = Radius of hemispherical part = r

Height of cylindrical part = r

As we know,

Volume of cylinder = πr^{2}h

Where r is base radius and h is height of cylinder.

Volume of cylindrical part = πr^{2}r = πr^{3} cm^{3}

Also,

, where r is radius of hemisphere.

Volume of conical part

Volume of building = Volume of cylindrical part + volume of conical part

Volume of building

Volume of air in building = volume of building

r^{3} = 8

r = 2 m

Height of building = 2r = 2(2) = 4 meter

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