$A$ cone and a cylinder having the same area of the base have also the same area of curved surfaces. If the height of the cylinder is $2 \, m$,find the slant height of the cone (in $m$).

The base of a right prism is an equilateral triangle with a side of $6 \, cm$. If the volume of the prism is $108 \sqrt{3} \, cm^3$,its height is ...... $cm$.

The sum of the radius of the base and the height of a solid cylinder is $37\, m$. If the total surface area of the solid cylinder is $1628\, m^2$,then the circumference of its base and the volume of the cylinder are:

The height of a right circular cone and the radius of its circular base are $9 \, cm$ and $3 \, cm$ respectively. The cone is cut by a plane parallel to its base so as to divide it into two parts. The volume of the frustum (i.e.,the lower part) of the cone is $44 \, cm^3$. The radius of the upper circular surface of the frustum $\left(\text{taking } \pi = \frac{22}{7}\right)$ is

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

If the base radius of a cone is increased by $20 \%$ and its slant height is doubled,then by what percentage will the area of its curved surface increase?