Question

A road 7 m wide surrounds a circular park whose circumference is 352 m. Find the area of the road.

Answer 1

Let the radius of the park be r metres.



Then, its circumference = $2\mathrm{\pi r}$
Therefore,
$2\mathrm{\pi r}=352\Rightarrow 2\times \frac{22}{7}\times \mathrm{r}=352$
$\Rightarrow \mathrm{r}=\left(352\times \frac{7}{44}\right)=56$
Thus, the inner radius = 56 m
Outer radius = (56 + 7) m = 63 m
Area of the road = $\mathrm{\pi }\left[{\left(63\right)}^2-{\left(56\right)}^2\right]$ m²
$=\frac{22}{7}\times \left(63+56\right)\left(63-56\right)$ m²
$=\left(\frac{22}{7}\times 119\times 7\right)$ m² = 2618 m²