A building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contains $41\frac{19}{21} {\mathrm{m}}^3$ of air. If the internal diameter of dome is equal to its total height above the floor, find the height of the building? $(\text{Use} \mathrm{\pi }=22/7)$

A building is in the form of a cylinder surmounted by a hemispherical dome. 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 $67\frac{1}{21} {\mathrm{m}}^3$ of air. $(\mathrm{Take} \mathrm{\pi } = 22/7)$

A solid toys in the form of a hemisphere surrounded by a right circular cone. The height of cone is $4 \mathrm{cm}$ and the diameter of the base is $8 \mathrm{cm}$. Determine the volume of the toy. If a cube circumscribes the toy, then find the difference of the volumes of cube and the toy. If the total surface area of the toy rounded off to two decimal places is $k {\mathrm{cm}}^2$ then find $k$..$(\text{Use} \mathrm{\pi }=22/7)$

The perimeters of the ends of a frustum of a right circular cone are $44 \mathrm{cm}$ and $33 \mathrm{cm}$. If the height of the frustum is $16 \mathrm{cm}$, find the slant surface and the total surface. $(\text{Use} \mathrm{\pi }=22/7)$ If the volume of the frustum is $k {\mathrm{cm}}^3$ then find $k$.