What is the length (in metre) of the longest rod that can be placed in a room which is $2$ $metre$ long,$2$ $metre$ broad,and $6$ $metre$ high?

How many small cubical blocks of side $5\, cm$ can be cut from a cubical block whose each edge measures $20\, cm$?

$A$ rectangular tank is $30\,m$ long and $20\,m$ broad. Water is being flown into it through a square pipe of side $5\,cm$. What is the speed of water if the level of water in the tank rises by $1\,m$ in $8\,hours$? (in $km/h$)

If the volumes of two cubes are in the ratio $27: 1$,the ratio of their edges is

$A$ sphere is melted to form a cylinder whose height is $4 \frac{1}{2}$ times its radius. What is the ratio of the radius of the sphere to the radius of the cylinder?

The base of a right prism is a quadrilateral $ABCD$. Given that $AB = 9\, cm$,$BC = 14\, cm$,$CD = 13\, cm$,$DA = 12\, cm$ and $\angle DAB = 90^{\circ}$. If the volume of the prism is $2070\, cm^3$,then the area of the lateral surface is........$cm^2$.