The area of the floor of a rectangular hall of length $40\, m$ is $960\, m^{2}$. Carpets of size $6\, m \times 4\, m$ are available. How many carpets are required to cover the hall?

The perimeter of a square is equal to twice the perimeter of a rectangle of length $8\, cm$ and breadth $7\, cm$. What is the circumference of a semicircle whose diameter is equal to the side of the square? (rounded off to the two decimal places) (in $cm$)

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.........$cm/sec$.

The length of a rectangle is twice its breadth. If its length is decreased by $5\, cm$ and breadth is increased by $5\, cm$,the area of the rectangle is increased by $75\, cm^2$. Then the length of the rectangle is......$cm$.

$A$ rope,by which a horse is tied,is increased from $12 \ m$ to $23 \ m$. How much additional ground will it be able to graze? (in $m^2$)

The circumference of $2$ circles is $88 \, m$ and $220 \, m$ respectively. What is the difference between the area of the larger circle and the smaller circle? (in $m^2$)