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

The length of one pair of opposite sides of a square is increased by $5 \, cm$ on each side,the ratio of the length and the breadth of the newly formed rectangle becomes $3:2$. What is the area of the original square? (in $cm^2$)

For a triangle whose sides are $50\, m$,$78\, m$,and $112\, m$ respectively,the length of the perpendicular from the opposite angle to the side $112\, m$ is ......... $m$.

The area of a rectangular football field is $24200 \ m^2$. Its breadth is half of its length. What is the approximate minimum distance a man will cover if he wishes to go from one corner to the opposite corner? (in $m$)

In the given figure,there is a large semicircle with diameter $AB = 56 \ cm$. Inside this,there are four smaller identical semicircles with diameters $AE, EF, FG,$ and $GB$ along the diameter $AB$. $A$ circle is inscribed such that it is tangent to the large semicircle and the two middle smaller semicircles. What is the area (in $cm^2$) of the shaded region?

Wheels of diameters $7\, cm$ and $14\, cm$ start rolling simultaneously from $X$ and $Y$,which are $1980\, cm$ apart,towards each other in opposite directions. Both of them make the same number of revolutions per second. If both of them meet after $10\, seconds$,the speed of the smaller wheel is.........$cm/sec$.