The surface area of a sphere is $5544 \, cm^2$. Find its volume in $cm^3$.

The front compound wall of a house is decorated by wooden spheres of diameter $21\, cm,$ placed on small supports as shown in the figure. Eight such spheres are used for this purpose,and are to be painted silver. Each support is a cylinder of radius $1.5\, cm$ and height $7\, cm$ and is to be painted black. Find the cost of paint required if silver paint costs $25$ paise per $cm^{2}$ and black paint costs $5$ paise per $cm^{2}.$

$A$ conical tent is made from a piece of cloth with an area of $165 \, m^{2}$. The radius of the base of the tent is $5 \, m$.
$(i)$ If one student occupies an average of $\frac{5}{7} \, m^{2}$ of ground area,how many students can sit in the tent?
$(ii)$ Find the volume of the cone.

The total surface area of a closed cylinder is $748\, cm^2$. If its radius is $7\, cm$,find its height (in $cm$).

The curved surface area of a cylinder is $550 \, cm^2$. If its height is $50 \, cm$,find its diameter in $cm$.

$A$ right triangle with sides $6 \, cm$,$8 \, cm$,and $10 \, cm$ is revolved about the side $8 \, cm$. Find the curved surface area of the solid so formed (in $cm^2$). (in $, cm^2$)