The area of a circle is $154 \, cm^{2}$. The length of an arc of the circle which subtends an angle of $45^{\circ}$ at the centre is......$cm$.

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

$A$ 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 $.5$)

$A$ circle and a rectangle have the same perimeter. The sides of the rectangle are $18 \, cm$ and $26 \, cm$. What is the area of the circle? (in $cm^2$)

The area of a quadrilateral is $420 \, m^{2}$ and the perpendiculars drawn to one diagonal from the opposite vertices are $18 \, m$ and $12 \, m$. Then,the length of the diagonal is......$m$

An open box is made of wood $2\, cm$ thick. Its internal length is $86\, cm,$ breadth $46\, cm$ and height is $38\, cm.$ The cost of painting the outer surface of the box at $Rs.$ $10$ per $m^2$ is? (in $Rs.$)