The respective ratio of the curved surface area and total surface area of a cylinder is $4:5$. If the curved surface area of the cylinder is $1232 \, cm^2$,what is the height? (in $cm$)

$A$ prism with a right triangular base is $25\, cm$ high. If the shorter sides of the triangle are in the ratio of $1: 2$ and the volume of the prism is $100\, cm^3$, what is the length of the longest side of the triangle?

$5$ 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 $m$)

The area of the iron sheet required to prepare a cone $24 \text{ cm}$ high with base radius $7 \text{ cm}$ is .......... $\text{cm}^2$ (Take $\pi = \frac{22}{7}$)

$A$ right circular cone is $3.6 \ cm$ high and the radius of its base is $1.6 \ cm$. It is melted and recast into a right circular cone with a base radius of $1.2 \ cm$. The height of the new cone (in $cm$) is:

The height of a cone is $30 \, cm$. $A$ small cone is cut off at the top by a plane parallel to the base. If its volume is $\frac{1}{27}$ of the volume of the given cone,at what height above the base is the section made? (in $cm$)