The length of an edge of a hollow cube opened at one face is $\sqrt{3}$ metres. What is the length of the largest pole that it can accommodate?

$A$ rectangular block of metal has dimensions $21\, cm$, $77\, cm$, and $24\, cm$. The block is melted into a sphere. The radius of the sphere is .......... $cm$. (Take $\pi = \frac{22}{7}$)

$A$ cylindrical can with a horizontal base and an internal radius of $3.5 \, cm$ contains sufficient water so that when a solid sphere is placed inside,the water just covers the sphere. The sphere fits exactly into the can. The depth of the water in the can before the sphere was added is:

Find out the amount of concrete required to erect a concrete pillar whose circular base has a perimeter of $8.8\, m$ and whose curved surface area is $17.6\, m^2$. $\left(\pi=\frac{22}{7}\right)$

$A$ solid cone of height $24 \, cm$ and base radius $8 \, cm$ is melted to form a solid cylinder of radius $6 \, cm$ and height $6 \, cm$. In the whole process,what percent of material is wasted (in $\%$)?

$5$ persons will live in a tent. If each person requires $16\, m^2$ of floor area and $100\, m^3$ space for air,then the height of the cone of smallest size to accommodate these persons would be? (in $m$)