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 $cm$)

Find the amount of water displaced by a solid spherical ball of diameter $4.2 \, cm$,when it is completely immersed in water. (in $, cm^3$)

The radius of a sphere is $6\, cm$. It is melted and drawn into a wire of diameter $1\, cm$. Find the length of the wire (in $m$).

The volume of a sphere is $4500 \pi \text{ cm}^3$,then its diameter is $\dots \text{ cm}$.

The curved surface area of a cone is $550 \, cm^2$. If the radius of the cone is $7 \, cm$,find its volume in $cm^3$.