If the area of a square is $50$ $sq$ units,then the area of the circle drawn on its diagonal is

$A$ is the centre of a circle whose radius is $8$ and $B$ is the centre of a circle whose diameter is $8$. If these two circles touch externally,then the area of the circle with diameter $AB$ is $.........\pi$.

The smallest side of a right-angled triangle is $8\, cm$ less than the side of a square of perimeter $56\, cm$. The second largest side of the right-angled triangle is $4\, cm$ less than the length of the rectangle of area $96\, cm^2$ and breadth $8\, cm$. What is the largest side of the right-angled triangle? (in $cm$)

$A$ hemispherical bowl of internal diameter $54 \ cm$ contains a liquid. The liquid is to be filled in cylindrical bottles of radius $3 \ cm$ and height $9 \ cm$. How many bottles are required to empty the bowl?

If a regular hexagon is inscribed in a circle of radius $r,$ then its perimeter is........$r$.

$A$ playground is in the shape of a rectangle. $A$ sum of ₹ $1,000$ was spent to make the ground usable at the rate of $25$ $paisa$ per $m^2$. The breadth of the ground is $50\, m$. If the length of the ground is increased by $20\, m$,what will be the expenditure in rupees at the same rate per $m^2$?