The radii of two cones are in the ratio $2:1,$ and their volumes are equal. Find the ratio of their heights.

The base of a $10\, cm$ high solid cylinder is a semi-circle of radius $7\, cm$. Its total surface area (in $cm^2$) is (Use $\pi = \frac{22}{7}$)

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

$A$ 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 $\pi = \frac{22}{7}$)

$66 \text{ cm}^3$ of silver is drawn into a wire $1 \text{ mm}$ in diameter. The length of the wire in metres will be

$A$ 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?