$A$ right triangle $ABC$ with sides $5 \, cm, 12 \, cm$ and $13 \, cm$ is revolved about the side $12 \, cm$. Find the volume of the solid so obtained.

At a Ramzan Mela,a stall keeper in one of the food stalls has a large cylindrical vessel of base radius $15 \, cm$ filled up to a height of $32 \, cm$ with orange juice. The juice is filled in small cylindrical glasses (see figure) of radius $3 \, cm$ up to a height of $8 \, cm$,and sold for $Rs. 15$ each. How much money does the stall keeper receive by selling the juice completely?

Find the total surface area of a cone,if its slant height is $21 \, m$ and diameter of its base is $24 \, m$. (Take $\pi = \frac{22}{7}$) (in $, m^2$)

The diameter of the moon is approximately one-fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?

The diameter of a roller is $84\, cm$ and its length is $120\, cm$. It takes $500$ complete revolutions to move once over to level a playground. Find the area of the playground in $m^2$. $\left[\text{Assume } \pi = \frac{22}{7}\right]$ (in $, m^2$)

Curved surface area of a cone is $308 \, cm^2$ and its slant height is $14 \, cm$. Find $(i)$ radius of the base and $(ii)$ total surface area of the cone.