The interior of the building is in the form of cylinder surmounted by a hemispherical dome, the base diameter of the dome is 4m and total height of the building is equal to 3/2 of the diameter of the dome
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Step-by-step explanation:
Height of building = height of cylinder + height of hemisphere
H=h+r
r is radius of cylinder and dome
diameter of dome =2/3× height of building
∴2r=32×(h+r)
∴6r=2h+2r ∴3r=h+r
∴h=2r
Volume of air in building = Volume of cylinder+ Volume of dome
∴67211=πr2h+32πr3
∴211408=πr2(h+32r)
=πr2(2r+2/3r)
=πr2(38r)
∴211408=38πr3
∴71408=8×722×r3
∴r3=22×8
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