The radius of a cylinder is the same as that of a sphere. Their volumes are equal. The height of the cylinder 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 $m$)

$A$ tent is in the shape of a right circular cylinder up to a height of $3\, m$ and then becomes a right circular cone with a maximum height of $13.5\, m$ above the ground. If the radius of the base is $14\, m$,find the cost of painting the inner side of the tent at the rate of ₹ $2$ per $m^2$ (in ₹).

$A$ 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 $km/h$)

$A$ solid cylinder has a total surface area of $231 \, cm^2$. Its curved surface area is $(2/3)$ of the total surface area. Find the volume of the cylinder (in $cm^3$).

How many small cubes,each of $96\,cm^{2}$ surface area,can be formed from the material obtained by melting a larger cube with $384\,cm^{2}$ surface area?