In the auditorium,there are $20$ cylindrical pillars. Each pillar has a radius of $14 \, cm$ and a height of $5 \, m$. Find the cost of painting the curved surface of all the pillars at the rate of ₹ $120$ per $m^2$.

The length and breadth of a cuboid are $30\, cm$ and $25\, cm$. If the total surface area of the cuboid is double the lateral surface area of the cuboid,find its height and volume.

State whether the following statement is true or false:
The lateral surface area of a cube with an edge length of $5 \, cm$ is $150 \, cm^2$.

The radius and slant height of a cone are in the ratio of $5:13$. If its curved surface area is $1836.9 \, cm^2$,find its volume. (Use $\pi = 3.14$) (in $cm^3$)

$A$ cylindrical container of radius $14\, cm$ is partially filled with water. $A$ solid cuboid of iron with dimensions $22\, cm \times 16\, cm \times 7\, cm$ is submerged in it. Find the rise in the level of the water when the solid is completely submerged. (in $cm$)

Curved surface area of a cone $= \dots$