In the figure,$ABCD$ is a trapezium with $AB \parallel DC$,$AB = 18 \, cm$,$DC = 32 \, cm$,and the distance between $AB$ and $DC = 14 \, cm$. If arcs of equal radii $7 \, cm$ with centers $A, B, C$,and $D$ have been drawn,find the area of the shaded region of the figure (in $cm^2$).

It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters $16 \, m$ and $12 \, m$ in a locality. The radius of the new park would be (in $m$)

In a circle,the length of a minor arc is $110 \,cm$ and it subtends an angle of measure $150^{\circ}$ at the centre. Then,the radius of the circle is $\ldots \ldots \ldots \ldots \,cm$.

As shown in the diagram,the side length of square garden $ABCD$ is $60\, m$. Flower beds are prepared in the shape of circular segments on two opposite sides of the square. The centre of the circles for these segments is the point of intersection $O$ of the diagonals of square $ABCD$. Find the total area of the two flower beds. (Use $\pi=3.14$) (in $m^2$)

The radius of a circular ground is $63 \, m$. Find the cost of fencing its boundary at the rate of ₹ $50 / m$. Find the cost of levelling the ground at the rate of ₹ $40 / m^2$.

The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters $36 \, cm$ and $20 \, cm$ is (in $cm$)