Two circles touch each other externally. The sum of their areas is $130 \pi \text{ cm}^2$ and the distance between their centres is $14 \text{ cm}$. The radius of the smaller circle is . . . . . . $\text{cm}$.

The perimeter of a square is double the perimeter of a rectangle. The area of the rectangle is $240 \, cm^2$. What is the area of the square? (in $cm^2$)

If the length and breadth of a rectangular plot are increased by $50 \%$ and $20 \%$ respectively,then how many times will its area be increased?

$A$ rectangular plot has a concrete path running in the middle of the plot parallel to the breadth of the plot. The rest of the plot is used as a lawn,which has an area of $240 \, m^2$. If the width of the path is $3 \, m$ and the length of the path is greater than its breadth by $2 \, m$,what is the area of the rectangular plot (in $m^2$)?

$A$ copper sphere of diameter $18\, cm$ is drawn into a wire of diameter $40\, mm$. Then,the length of the wire is......$cm$?

Three medians $AD, BE$ and $CF$ of $\Delta ABC$ intersect at $G.$ The area of $\Delta ABC$ is $36 \text{ cm}^2$. Then the area of $\Delta CGE$ is (in $\text{cm}^2$)