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......$cm$.

The surface area of a spherical part of a bowl with a flat circular detachable cover,excluding the cover,is $616 \, cm^2$. The area of the cover is $38.5 \, cm^2$. What is the volume of the bowl? (in $cm^3$)

If the circumference of a circle is equal to the perimeter of a square,what is the ratio of the area of the circle to the area of the square?

The ratio of the $3$ angles of a quadrilateral is $13: 9: 5$. The value of the $4^{th}$ angle of the quadrilateral is $36^{\circ}$. What is the difference between the largest and the second smallest angles of the quadrilateral? (in $^{\circ}$)

If the length of a rectangular field is increased by $20 \%$ and the breadth is reduced by $20 \%,$ the area of the rectangle will be $192 \, m^2.$ What is the area of the original rectangle? (in $m^2$)

The perimeter of an isosceles triangle is $306\, m$ and each of the equal sides is $\frac{5}{8}$ of the base. Find the area.