The radii of two cylinders are in the ratio of $2:3$ and their heights are in the ratio of $5:3$. The ratio of their volumes is

$A$ 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?

The surface area of a sphere is $2464 \, cm^2$. Find its diameter 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 $, cm^3$)

Write True or False and justify your answer.
An edge of a cube measures $r \, cm$. If the largest possible right circular cone is cut out of this cube,then the volume of the cone (in $cm^3$) is $\frac{1}{6} \pi r^3$.

$A$ cone of height $12 \, cm$ has a volume $616 \, cm^3$. Then its diameter is $\ldots \ldots \ldots \, cm$.