Question

# A building is in the form of a cylindrer surmounted by a hemispherical vaulted dome and contains 411921m3 of air.If the internal diameter of dome id equal to its total height above the floor,find the height of the building?

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Solution

## Let R be the radius, and h be the height of the cylindrical portion. Height of the building, R+h = 2R = D = internal diameter. ⇒ h = R. Volume = Volume of cylindrical portion + Volume of hemispherical portion ⇒ πR2h+43πR32=88021 ⇒ 227(R2h+2R33)=88021 ⇒R2(h+2R3)=403 ⇒ R2(R+2R3)=403 ⇒R3(53)=403 ⇒R3=8 ∴R = 2 m and Total Height of the building, = R+h = 2R=2(2) = 4 m

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