An isosceles right-angled triangle has an area of $200 \, cm^2$. The length of its hypotenuse is ..... $cm$.

The area of the largest circle that can be drawn inside a rectangle with sides $18 \, cm$ and $14 \, cm$ is (in $cm^2$):

$A$ conical iron piece having diameter $28 \, cm$ and height $30 \, cm$ is totally immersed into the water of a cylindrical vessel,resulting in the rise of water level by $6.4 \, cm$. The diameter,in $cm$,of the vessel is

The sides of a triangle are $50 \, cm$,$78 \, cm$,and $112 \, cm$. The smallest altitude is $........... \, cm$.

$A$ sphere of $30 \ cm$ radius is dropped into a cylindrical vessel of $80 \ cm$ diameter,which is partly filled with water. If its level rises by $x \ cm$,find $x$ (in $cm$). (in $.5$)

The area of a square is $1444 \ m^2$. The breadth of a rectangle is $\frac{1}{4}$ of the side of the square and the length of the rectangle is thrice its breadth. What is the difference between the area of the square and the area of the rectangle? (in $m^2$)