Question

A path of width $3.5$ m runs around a semi-circular grassy plot whose perimeter is $72$ m. Find the area of the path. (Use $\pi$ $=\frac{22}{7}$).

Answer 1

Perimeter of plot$=72m$

$\Rightarrow \pi r+2r=72m\Rightarrow r[\frac{22}{7}+2]=72\Rightarrow r=\frac{72\times 7}{36}=14m$

$\Rightarrow$ Width of path$=3.5m$

$\Rightarrow$Outer radius, $R=14+3.5=17.5m$

Area of path$=\frac{1}{2}\pi (R^2-r^2)=\frac{1}{2}\times \frac{22}{7}({17.5}^2-{14}^2)=173.25m^2$