$5$ 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 $m$)

Find the diagonal of a cuboid whose dimensions are $12\, m$ by $10\, m$ by $8\, m$.

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........$cm^2$.

The base of a right pyramid is an equilateral triangle of side $4 \text{ cm}$. The height of the pyramid is half of its slant height. Its volume is ........ $\text{cm}^3$.

How many bricks are required to build a $15\, m$ long,$3\, m$ high,and $50\, cm$ thick wall,if each brick measures $25\, cm \times 12\, cm \times 6\, cm$?

From a cubical block of wood of side $1 \, m$,a cylinder of the largest possible volume is carved out. The volume (in $m^3$) of the remaining wood is