Question

All the arcs in following diagram are semicircles. This diagram shows two paths connecting Ato B. Path I is the single large semi-circle and Path II consists of the chain of small semi-circles.

• A. Path I is longer than path II
• B. Path I is of the same length as Path II
• C. Path I is shorter than Path II
• D. Path I is of the same length as Path II, only if the number of semicircles is not more than 4

Answer 1

The correct option is B Path I is of the same length as Path II

Let the number of small semicircle be n
Path I= $\pi$ R = n $\pi$ r
Path II=n ($\pi$ r)
So,Path I = Path II