Question

The length of an arc of a circle is 4 centimetres, what is the length of an arc of the same central angle, in a circle of double the radius?

Answer 1

Let the radius of the first circle be r.

Let the central angle made by the arc be of 360°.

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

⇒ 4 cm = × 2πr …(1)

Radius of the second circle = 2r

Given: The central angle of both the circles is same.

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

= × 2π(2r)

= 2 × × 2πr

= 2 × 4 cm (From (1))

= 8 cm