The length of the diagonal of a cube is $6 \text{ cm}$. The volume of the cube (in $\text{cm}^3$) is (in $\sqrt{3}$)

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

$5$ 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 $m$)

If $h, c, v$ are respectively the height,curved surface area,and volume of a right circular cone,then the value of $3 \pi v h^{3} - c^{2} h^{2} + 9 v^{2}$ is

$A$ $3.3\, m$ high room is half as long again as it is wide and its volume is $123 \frac{3}{4}\, m^3$. Find its length and breadth.

What is the curved surface area (in $cm^2$) of a cylinder having radius of base as $14 \, cm$ and height as $10 \, cm$?