$A$ solid metallic sphere of radius $21\, cm$ is melted and recast into a cone with diameter of the base as $21\, cm$. What is the height (in $cm$) of the cone?

$A$ wire bent in the form of a circle of radius $42 \, cm$ is bent in the form of a rectangle whose sides are in the ratio of $6:5$. The smaller side of the rectangle is (in $cm$)

The ratio between the areas of two circles is $4: 7.$ What will be the ratio of their radii?

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 area of the circumcircle of an equilateral triangle is $3 \pi \, cm^2$. The perimeter of the triangle is

$A$ room is $7 \text{ m}$ long and $5 \text{ m}$ broad. The doors and windows occupy $5 \text{ m}^2$. The cost of papering the remaining part of the walls with paper $75 \text{ cm}$ wide,at ₹ $4.20$ per piece of $13 \text{ m}$,is ₹ $39.20$. Find the height of the room (in $\text{m}$).