Question

Four identical circlular lands are crossing each other as shown. All the arcs are 4 m long. What is the length of fence around one complete circular land?

• A. 24 m
• B. 32 m
• C. 36 m
• D. 28 m

Answer 1

The correct option is B 32 m

In one quarter of circle, there is one 4 m arc and two 2 m arcs. So, effectively, there are two 4 m arcs.

Hence, one 4 m arc is half of ${90}^{\circ }$, i.e., ${45}^{\circ }$

1 whole angle of circle = ${360}^{\circ }$
Total number of ${45}^{\circ }$ angles = $\frac{{360}^{\circ }}{{45}^{\circ }}=8$

Circumference = Length of fence needed = $8\times 4m=32m$