Question

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.

Answer 1

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