The volume of a right circular cone is $9856 \, cm^3$. If the diameter of the base is $28 \, cm$,find the slant height of the cone. (in $, cm$)

$A$ 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. Also,find the volume of the solid obtained when the same triangle is revolved about the side $5 \, cm$. Finally,find the ratio of the volumes of the two solids.

Write True or False and justify your answer.
An edge of a cube measures $r \, cm$. If the largest possible right circular cone is cut out of this cube,then the volume of the cone (in $cm^3$) is $\frac{1}{6} \pi r^3$.

The height of a cone is $15 \, cm$. If its volume is $1570 \, cm^3$,find the radius of the base. (Use $\pi = 3.14$) (in $, cm$)

The radius and slant height of a conical vessel are $21 \,cm$ and $29 \,cm$ respectively. What is its capacity in litres?

Find the capacity in litres of a conical vessel with radius $7 \, cm$ and slant height $25 \, cm$. (in $, l$)