16. Exemplar Example Problems V

A building is in the form of a cylinder surmounted by a hemispherical dome (see Fig.). The base diameter of the dome is equal to \(\frac{2}{3}\) of the total height of the building. Find the height of the building, if it contains \(67\frac{1}{21}\) \(m^3\) of air.

 

 

Required height \(=\) \(m\)