Question

A building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contains $41\frac{19}{21}{m}^3$ of air. If the internal diameter of dome is equal to its total height above the floor, find the height of the building.

• A. $4m$
• B. $8m$
• C. $6m$
• D. $10m$

Answer 1

The correct option is A $4m$

Diameter of hemisphere $\left(D\right)=$ Total height of building $\left(H\right)$

Radius of hemisphere $\left(R\right)=\frac{H}{2}=$ Height of the hemisphere
Height of cylinder $=H-\frac{H}{2}=\frac{H}{2}$

Volume of building $=$ Vol. of cylinder $+$ Vol. of hemisphere

$\frac{880}{21}=\pi r^{2}H+\frac{2}{3}\pi r^3$

$\frac{880}{21}=\pi {\left(\frac{H}{2}\right)}^3+\frac{2}{3}\pi {\left(\frac{H}{2}\right)}^3$

$H=4$ m