$A$ 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 $.5$)

$A$ can go round a circular path $8$ times in $40$ minutes. If the diameter of the circle is increased to $10$ times the original diameter,then the time required by $A$ to go round the new path once,travelling at the same speed as before,is (in $min$)

The ratio of length and breadth of a rectangular plot is $8:5$ respectively. If the breadth is $60\, m$ less than the length,what is the perimeter of the rectangular plot? (in $m$)

How many times will a wheel of diameter $105\, cm$ rotate in covering a distance of $330\, m$? (in $revolutions$)

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

The circumference of a circle whose area is $24.64\, m^{2}$ is ....... $m$.