Question

A room in the form of a cylinder, surmounted by a hemispherical vaulted dome, contains 41 19/21 m³ of air and the internal diameter of the building is equal to the height of the crown of the vault above the floor. Find the height.

Answer 1

Let r be the radius of hemisphere and cylinder

and height of the cylinder = h

Given: Volume of air = 880/21 m³

∴ Diameter of the building = 2r

Height of the building (H) = diameter of the building

∴ Height of the cylinder + Radius of hemispherical dome = 2r

⇒ h + r = 2r

⇒ h = 2r – r

⇒ h = r

Volume of air inside the building = Volume of hemispherical portion + Volume of cylindrical portion

⇒ r³ = 8

⇒ r = 2

⇒ Height of building = 2r = 2×2 = 4m

Hence, the total height of the building is 4m.