Prove that the surface area of a sphere is equal to the curved surface area of the circumscribed cylinder.

A circus tent has cylindrical shape surmounted by a conical roof. The radius of the cylindrical base is $20 \mathrm{m}.$ The heights of the cylindrical and conical portions are $4.2 \mathrm{m}$ and $2.1 \mathrm{m}$, respectively. Find the volume of the tent. $(\mathrm{Take} \mathrm{\pi }=22 / 7 )$

A boiler is in the form of a cylinder $2 \mathrm{m}$ long with hemispherical ends each of $2$ meter diameter. Find the volume of the boiler. $(\mathrm{Take} \mathrm{\pi }=22 / 7 )$

A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is $104 \mathrm{cm}$ and the radius of each of the hemispherical ends is $7 \mathrm{cm}$. Find the cost of polishing its surface at the rate of $₹10 \mathrm{per} {\text{dm}}^2.$ $(\mathrm{Take} \mathrm{\pi }=3.14)$

A vessel in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is $14 \mathrm{cm}$ and the total height of the vessel is $13 \mathrm{cm}.$ Find the inner surface area of the vessel. $(\mathrm{Take} \mathrm{\pi }=22 / 7 )$

A solid iron pole having a cylindrical portion $110 \mathrm{cm}$ high and of base diameter $12 \mathrm{cm}$ is surmounted by a cone $9 \mathrm{cm}$high. Find the mass of the pole, given that the mass of  $1 {\mathrm{cm}}^3$ of iron is $8 \mathrm{gm}$. $(\text{Use} \mathrm{\pi }=22/7)$