If $D, E$ and $F$ are the mid-points of the sides of an equilateral triangle $ABC,$ then the ratio of the area of triangle $DEF$ and $DCF$ is

If the curved surface area of a cone is thrice that of another cone and the slant height of the second cone is thrice that of the first,find the ratio of the area of their bases. (in $:1$)

The circumference of a circle whose area is $24.64\, m^{2}$ is ....... $m$.

The radius of a coin is $1\, cm$. If four of these coins are placed on a table so that the rim of each touches that of the other two,find the area of the unoccupied space between them. (in $cm^2$)

$A$ piece of wire $132 \, cm$ long is bent successively in the shapes of an equilateral triangle,a square,a regular hexagon,and a circle. Then,which has the largest surface area?

Three metal cubes with edges $6\, cm$,$8\, cm$,and $10\, cm$ respectively are melted together and formed into a single cube. Find the side of the resulting cube (in $cm$).