Find the amount of water displaced by a solid spherical ball of diameter $28 \, cm$.

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 $m$)

The radius of a spherical balloon increases from $7 \, cm$ to $14 \, cm$ as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.

Find the total surface area of a cone,if its slant height is $21 \, m$ and diameter of its base is $24 \, m$. (Take $\pi = \frac{22}{7}$) (in $, m^2$)

$A$ 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.

$A$ 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 $m^2$. $\left[ \text{Assume } \pi = \frac{22}{7} \right]$