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 $, m^2$)

Savitri had to make a model of a cylindrical kaleidoscope for her science project. She wanted to use chart paper to make the curved surface of the kaleidoscope (see figure). What would be the area of chart paper required by her,if she wanted to make a kaleidoscope of length $25\, cm$ with a $3.5\, cm$ radius (in $, cm^{2}$)? You may take $\pi=\frac{22}{7}$.

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?

$A$ corn cob (see figure),shaped somewhat like a cone,has the radius of its broadest end as $2.1\, cm$ and length (height) as $20\, cm$. If each $1\, cm^2$ of the surface of the cob carries an average of four grains,find how many grains you would find on the entire cob.

The length,breadth,and height of a room are $5\, m$,$4\, m$,and $3\, m$ respectively. Find the cost of whitewashing the walls of the room and the ceiling at the rate of $Rs. 7.50$ per $m^2$.