The formula to find the total surface area of a $5$-rupee coin is $A = \ldots$

$A$ cone of radius $8 \, cm$ and height $12 \, cm$ is divided into two parts by a plane through the mid-point of its axis parallel to its base. Find the ratio of the volumes of the two parts.

The curved surface area $(CSA)$ of a cone is $\ldots \ldots$

The volume of a sphere with radius $1.5 \text{ cm}$ is $\ldots \ldots \ldots \text{ cm}^3$.

The volume of a sphere is $\ldots \ldots \ldots$

$A$ 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 the dome is equal to its total height above the floor,find the height of the building? (in $m$)