The area of a circular park is 12474 m$$^2$$ . There is 3.5 m wide path around the park. What is the area (in m$$^2$$) of the path?(Take $$\pi = \frac{22}{7}$$)

Let the radius of the circular park = r

Area of a circular park is 12474 m$$^2$$.

$$\frac{22}{7}r^2=12474$$

$$r^2=567\times7$$

$$r^2=81\times7\times7$$

$$r=63$$ m

Area of the circular width = Area of outer circle - Area of the inner circle

= $$\frac{22}{7}\times66.5^2-\frac{22}{7}\times63^2$$

= $$\frac{22}{7}\left[66.5^2-63^2\right]$$

= $$\frac{22}{7}\ \times129.5\times3.5$$

= 1424.5 m$$^2$$

Hence, the correct answer is Option A