The total surface area of a hemisphere is $41.58 \text{ cm}^2$. Find its curved surface area (in $\text{cm}^2$).

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

If the volume of a sphere is numerically equal to its surface area,then its diameter is ......... $cm$.

$A$ rectangular sheet of area $264 \text{ cm}^2$ and width $11 \text{ cm}$ is rolled along its breadth to make a hollow cylinder. The volume of the cylinder is (in $\text{cm}^3$):

$A$ hemisphere is made of lead. Its radius is $6 \, cm$. It is cast into a right circular cone of $75 \, cm$ height. The radius of the base of the cone is ......... $cm$.

$A$ school room is to be built to accommodate $70$ children,so as to allow $2.2\, m^2$ of floor area and $11\, m^3$ of space for each child. If the room is $14\, m$ long,what must be its breadth and height?