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 cost of carpeting a room $5 \ m$ wide with carpet at ₹ $3.50$ per $m^2$ is ₹ $105$. The length of the room is ...... $m$.

The volume of a cylinder is $448 \pi \, cm^3$ and its height is $7 \, cm$. What are its lateral surface area and total surface area?

Two roads $XY$ and $YZ$ of $15 \ m$ and $20 \ m$ length respectively are perpendicular to each other. What is the distance between $X$ and $Z$ by the shortest route? (in $m$)

$A$ rectangular park $60 \, m$ long and $40 \, m$ wide has two concrete crossroads running in the middle of the park, and the rest of the park has been used as a lawn. If the area of the lawn is $2109 \, m^2$, then what is the width of the road? (in $m$)

$A$ rectangular sheet of cardboard is of $4 \, cm \times 2 \, cm$. If a circle of the greatest possible area is cut from it,then the area of the remaining portion is: