Question

In a circle, the length of an arc of central angle 40° is 3 centimetres. What is the perimeter of the circle? What is its radius?

Answer 1

Central angle made by the given arc is 40°, which is of 360°.

∴ Length of the arc = of the perimeter of the circle

⇒ 3 cm = × Perimeter of the circle

⇒ Perimeter of the circle = (3 × 9) cm

= 27 cm

Let the radius of the given circle be r cm.

∴ 2πr = 27 cm

⇒ 2 × 3.141 × r = 27 cm

⇒ 6.282 × r = 27

⇒ r = 4.3 cm