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?
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