The curved surface area of a cylinder is $1320 \, cm^2$. If its height is $30 \, cm$,find its diameter (in $cm$).

If the total surface area of a cone is $3696 \, cm^{2}$ and the curved surface area of a cone is $2310 \, cm^{2}$,find the ratio of the radius to the slant height.

The curved surface area of a cylinder is $550 \, cm^2$. If its height is $50 \, cm$,find its diameter in $cm$.

$A$ school provides milk to the students daily in cylindrical glasses of diameter $7 \, cm$. If the glass is filled with milk up to a height of $12 \, cm$, find how many litres of milk is needed to serve $1600$ students.

Write True or False and justify your answer in each of the following:
The volume of the largest right circular cone that can be fitted in a cube whose edge is $2r$ is equal to the volume of a hemisphere of radius $r$.

$A$ metal sphere with a radius of $12\, cm$ is melted,and recast into cones with radius $3\, cm$ and height $4\, cm$. Find how many cones are obtained?