The diameter of each wheel of a vehicle is $42 cm$. Each wheel makes $20$ revolutions in $12$ seconds. Find the speed of the vehicle in metre per minute.

The difference between the perimeter and the radius of a circle is $37 cm$. Find the area of the circle.

(Use $\mathrm{\pi }=\frac{22}{7}$)

In Figure, $OABC$ is a rhombus, three of whose vertices lie on a circle with centre $O$. If the area of the rhombus is $18\sqrt{3} c{m}^2$, find the perimeter and area of the circle [take $\mathrm{\pi }=3.14$].

If the areas of two concentric circles are $154 c{m}^2$ and $616 c{m}^2$ respectively, then find the width and area of the circular path between them.

(Take $\mathrm{\pi }=\frac{22}{7}$)

Find the area of the largest circle that can be drawn inside a square of side $21 cm$.

(Take $\mathrm{\pi }=\frac{22}{7}$)

The cost of levelling a path of uniform width which surrounds a circular park of diameter $320 m$ at the rate of $₹ 7.00$ per square metre is $₹ 35750$. Find the width of the path.

(Take $\mathrm{\pi }=\frac{22}{7}$)

The cost of fencing a circular field at the rate of $₹ 18.00$ per metre is $₹ 3960$. The field is to be levelled at the rate of $₹ 6.00$ per square metre. Find the cost of levelling.

(Take $\mathrm{\pi }=\frac{22}{7}$)