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.

Rain water which falls on a flat rectangular surface of length $6\, m$ and breadth $4\, m$ is transferred into a cylindrical vessel of internal radius $20\, cm$. What will be the height of water in the cylindrical vessel if the rainfall is $1\, cm$? Give your answer to the nearest integer. (Take $\pi = 3.14$) (in $cm$)

$A$ small village, having a population of $5000$, requires $130\, \text{litres}$ of water per head per day. The village has an overhead cuboidal tank measuring $20\, \text{m} \times 13\, \text{m} \times 10\, \text{m}$. For how many days will the water of this tank last?

For a given cylinder,the diameter of the base is $7 \,cm$ and its height is $12 \,cm$. Find the curved surface area of a cylinder (in $cm^2$).

$A$ room without a ceiling is $12 \, m$ long,$4 \, m$ wide,and $3 \, m$ high. Find the length of the longest rod that can be placed in that room. (in $m$)

Write True or False and justify your answer in each of the following: If the length of the diagonal of a cube is $6 \sqrt{3} \, \text{cm}$,then the length of the edge of the cube is $3 \, \text{cm}$.