If the lateral surface area of a cylinder is $94.2 \, cm^2$ and its height is $5 \, cm$,then find its volume. (Use $\pi = 3.14$) (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 $cm^2$.

$A$ cylindrical pillar is $50 \, cm$ in diameter and $3.5 \, m$ in height. Find the cost of painting the curved surface of the pillar at the rate of $Rs. \, 12.50$ per $m^2$. $\left[ \text{Assume } \pi = \frac{22}{7} \right]$

Twenty-seven solid iron spheres,each of radius $r$ and surface area $S$,are melted to form a single sphere with surface area $S^{\prime}$. Find the radius $r^{\prime}$ of the new sphere. (in $r$)

$A$ patient in a hospital is given soup daily in a cylindrical bowl of diameter $7 \, cm$. If the bowl is filled with soup to a height of $4 \, cm$, how much soup does the hospital have to prepare daily to serve $250$ patients?

Find the surface area of a sphere with a diameter of $3.5 \, cm$. Assume $\pi = \frac{22}{7}$. (in $, cm^2$)