If a piece of wire 136 cm long is bent into an arc of a circle subtending an angle of 108° at center, then radius of circle (in cm) is?
Answer & explanation
Correct answer: option 3
Length of wire = circumference of arc + 2 (radius)
⇒ 136 = 2πr\(\frac{Θ}{360}\) + 2r
⇒ 136 = (\(\frac{108}{360}\) π + 1) 2r
⇒ 136 = (\(\frac{3}{10}\) π + 1) 2r
⇒ 136 = (\(\frac{3}{10}\) × \(\frac{22}{7}\) + 1) 2r
⇒ 136 = (\(\frac{66}{70}\) + 1) 2r
⇒ 136 = \(\frac{136}{70}\) 2r
⇒ 70 = 2r
⇒ r = 35 cm