Area related to circles

Question

A path of $4$ m width runs round a semi circular grassy plot whose circumference is $163 \frac{3}{7}$ m find the area of the path. Well my answer is around $624$ $m^2$ but I have seen completely different answers as well. Say what's yours?

Answer 1

If the circumference is referred to the axis of the path we have that

• radius of the path $R=\frac{163 \frac{3}{7}}{\pi}=\frac{1144}{7\pi} m$
• area =$ \frac{\pi(R+2)^2}{2}-\frac{\pi(R-2)^2}{2}=\frac{4576}{7}\approx 653.7 m^2$