If the radius and slant height of a cone are in the ratio $7: 13$ and its curved surface area is $286 {\mathrm{cm}}^2,$ find its radius( in $\mathrm{cm}$).

Mark the correct alternative in each of the following:

The number of surfaces of a cone is

The area of the curved surface of a cone of radius $2r$ and slant height $\frac{l}{2},$ is

The total surface area of a cone of radius $\frac{r}{2}$ and length $2l$ , is

Mark the correct alternative in each of the following:

A solid cylinder is melted and cast into a cone of same radius. The heights of the cone and cylinder are in the ratio

Mark the correct alternative in each of the following:

If the radius of the base of a right circular cone is $3r$and its height is equal to the radius of the base, then its volume is