Question

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.

Answer 1

Radius of circular field, $r_1=105m$

Width of path $=5m$

$\therefore$ Radius of inner circle, $r_2=105-5=100m$

$\therefore$ Area of path $=\pi r_1^2-\pi r_2^2$

$=\frac{22}{7}\left[\right(105{)}^2-\left(100{)}^2\right]$

$=\frac{22}{7}(105+100)(105-100$

$=\frac{22}{7}\times 205\times 5$

$=\frac{22550}{7}{m}^2$

$=3221\frac{3}{7}{m}^2$