While calculating the area of a circle,its radius was taken to be $6 \, cm$ instead of $5 \, cm$. The calculated area is $\dots \%$ more than the actual area.

$A$ circular pond has a diameter of $17.5 \, m$. It is surrounded by a $2 \, m$ wide path. Find the cost of constructing the path at the rate of $Rs. \, 25$ per $m^2$ (in $Rs.$).

In a circle with radius $21 \ cm$,the perimeter of a minor sector is $64 \ cm$. Then,the length of the arc of that sector is $\ldots \ cm$.

In the figure,a square is inscribed in a circle of diameter $d$ and another square is circumscribing the circle. Is the area of the outer square four times the area of the inner square? Give reasons for your answer.

The areas of two sectors of two different circles are equal. Is it necessary that their corresponding arc lengths are equal? Why?

$A$ piece of wire $20 \,cm$ long is bent into the form of an arc of a circle subtending an angle of $60^{\circ}$ at its centre. Find the radius of the circle. (in $cm$)