Practicing Success
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? |
28 cm 44 cm 35 cm 14 cm |
35 cm |
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 |