Question

A path of width $3.5$ m runs around a semicircular grassy plot whose perimeter is $72m$. Find the area of the path (use $\pi =22/7$)

• A. $173m^2$
  
• B. $173.25m^2$
• C. $203m^2$
• D. $203.25m^2$

Answer 1

The correct option is B $173.25m^2$

As we know that perimeter of semi-circle $=\pi r+2r$

Perimeter of the given semiciruclar grassy plot $=72m$

$\therefore \pi r+2r=72$

$\Rightarrow \frac{22}{7}r+2r=72$

$\Rightarrow 22r+14r=504$

$\Rightarrow 36r=504\Rightarrow r=\frac{504}{36}=14m$

Area of semi-circle $=\frac{1}{2}\pi r^2$

As the radius of semi-circular plot $\left(r\right)=14m$

$\therefore$ Area of semi-circular plot $=\frac{1}{2}\times \frac{22}{7}\times {\left(14\right)}^2=308m^2$

As the path of width $3.5m$ is added around the semi-circular plot.

$\therefore$ Radius of whole area $=r+3.5=17.5m$

$\therefore$ Area of new semi-circle $=\frac{1}{2}\times \frac{22}{7}\times {\left(17.5\right)}^2=481.25m^2$

Now,

Area of path $=$ Area of new semicircle $-$ area of semi-circular plot

$\therefore$ Area of path $=481.25-308=173.25m^2$

Hence the area of path is $173.25m^2$