a building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contains 880 / 21 cu. m of air. If the internal diameter of the building is equal to its total height above the floor, find the height of the building.
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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 + (4πR³/3)/2 = 880/21
⇒(22/7)(R²h + 2R³/3) = 880/21
⇒R²(h+2R/3) = 440/3
⇒R²(R+2R/3) = 440/3
⇒R³(5/3) = 440/3
⇒R³ = 88
∴R = 4.45 m
and Total Height of the building, = R+h = 2R = 8.9 m
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