Q4 of 44 Page 14

A room in the form of a cylinder, surmounted by a hemispherical vaulted dome, contains 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


Let r be the radius of hemisphere and cylinder


and height of the cylinder = h


Given:


∴ 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.


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