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 $=$ $m$