Find the volume of a sphere whose radius is $7 \, cm$. Assume $\pi = \frac{22}{7}$.

It costs $Rs. 2200$ to paint the inner curved surface of a cylindrical vessel $10 \, m$ deep. If the cost of painting is at the rate of $Rs. 20$ per $m^2$, find the radius of the base. (in $m$)

$A$ wooden bookshelf has external dimensions as follows: Height $= 110\, cm$,Depth $= 25\, cm$,Breadth $= 85\, cm$ (see Fig.). The thickness of the plank is $5\, cm$ everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is $20$ paise per $cm^2$ and the rate of painting is $10$ paise per $cm^2$,find the total expenses required for polishing and painting the surface of the bookshelf.

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 $, m^2$)

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

Diameter of the base of a cone is $10.5\, cm$ and its slant height is $10\, cm$. Find its curved surface area. Assume $\pi = \frac{22}{7}$. (in $, cm^2$)