The circumference of a given circular park is 55 m. It is surrounded by a path of uniform width 3.5 m. Find the area of the path.

Let r be the radius of the circular park.

Circumference = 2πr

⇒ 2πr = 55

⇒ 2 x $\dfrac{22}{7}$ x r = 55

⇒ $\dfrac{44}{7}$ x r = 55

⇒ r = $\dfrac{7 \times 55}{44}$

⇒ r = $\dfrac{7 \times 5}{4}$

⇒ r = $\dfrac{35}{4}$

⇒ r = 8.75 m

Radius of outer park = radius of park + width of the path

= 8.75 + 3.5 m

= 12.25 m

Area of the path = Area of outer park - Area of circular park

= π (12.25)² - π (8.75)² m²

= 150.0625π - 76.5625π m²

= 73.5 π m²

= 73.5 x $\dfrac{22}{7}$ m²

= 10.5 x 22 m²

= 231 m²

Hence, the area of the path is 231 m².