A circular field of radius 105 m has a circular path of uniform width of 5 m along and inside its boundary. Find the area of the path.

Given:

Radius of outer circular field = 105 m

Radius of inner circular field = 105 - 5 m

= 100 m

Area of circular ring = Area of outer circular field - Area of inner circular field

As we know, the area of the circle = πr²

Area of circular ring =

$\dfrac{22}{7} \times 105^2 - \dfrac{22}{7} \times 100^2\\[1em] = \dfrac{22}{7} \times 11,025 - \dfrac{22}{7} \times 10,000\\[1em] = \dfrac{2,42,500}{7} - \dfrac{2,20,000}{7}\\[1em] = \dfrac{2,42,500 - 2,20,000}{7}\\[1em] = \dfrac{22,550}{7}\\[1em] = 3221\dfrac{3}{7} \text{ m}^2$

Hence, the area of circular field is $3221\dfrac{3}{7}$ m².