A conical hole is drilled in a circular cylinder of height $12 \mathrm{cm}$ and base radius $5 \mathrm{cm}.$ The height and the base radius of the cone are also the same. Find the whole surface area and volume of the remaining cylinder in terms of $\mathrm{\pi }$.

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 vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylinder is  $\frac{14}{3}$ $\mathrm{m}$ and the diameter of hemisphere is $3.5 \mathrm{m}$. Calculate the volume and the internal surface area of the solid. $(\mathrm{Take} \mathrm{\pi }=3.14)$

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 cylindrical vessel of diameter $14 \mathrm{cm}$ and height $42 \mathrm{cm}$ is fixed symmetrically inside a similar vessel of diameter $16 \mathrm{cm}$ and height $42 \mathrm{cm}$. The total space between the two vessels is filled with cork dust for heat insulation purposes. How many cubic centimeters of cork dust will be required? $(\mathrm{Take} \mathrm{\pi }=3.14)$

A cylindrical road roller made of iron is $1 \mathrm{m}$ long, Its internal diameter is $54 \mathrm{cm}$ and the thickness of the iron sheet used in making the roller is $9 \mathrm{cm}.$ Find the mass of the roller, if  $1 {\mathrm{cm}}^3$ of iron has $7.8 \mathrm{gm}$ mass. $(\text{ Use }\pi =3.14)$

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. $(\mathrm{Take} \mathrm{\pi }=22 / 7 )$