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 . $\left(\mathrm{Use}\mathrm{\pi }=\frac{22}{7}\right)$

Answer 1

Let the radius of the semicircular plot be r.
Perimeter of the semi-circular grassy plot = $\mathrm{\pi r}+2\mathrm{r}=72$
$\Rightarrow r=14\mathrm{cm}$
Given that the width of the plot = 3.5 m
Thus, the outer radius = 3.5 + 14 = 17.5 m
Area of the path = $\frac{{\mathrm{\pi R}}^2}{2}-\frac{{\mathrm{\pi r}}^2}{2}$
$$\begin{gathered} =\frac{\mathrm{\pi }}{2}\left(R^2-r^2\right) \\ =\frac{\mathrm{\pi }}{2}\left({\left(17.5\right)}^2-{\left(14\right)}^2\right) \\ =173.25{\mathrm{m}}^2 \end{gathered}$$