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.$(Use\pi =22/7)$

Answer 1

Let the radius of the semicircular grass plot be $r$

Now, perimeter of a semicircular grassy$=$Circumference of semicircular grassy plot$+$diameter of semicircular grassy plot.

$\Rightarrow 72=\frac{1}{2}\times 2\pi r+2r$

$\Rightarrow 72=\frac{36r}{7}$

$\Rightarrow r=14$m

Now, the distance $R$ of the circumference of the path from the centre is given by $14+3.5=17.5$m

Now, area of path$=\frac{\pi R^2}{2}-\frac{\pi r^2}{2}$

$=\frac{1}{2}\times \frac{22}{7}\times 17.5\times 17.5-\frac{1}{2}\times \frac{22}{7}\times 14\times 14$

$=481.25-308=173.25m^2$

Hence, the perimeter of a semicircular protractor is $173.25m^2$