Question

If a piece of wire 30cm long is bent into the form of an arc of a circle, subtending an angle of 60° at its centre, then radius of the circle is :​

Answer 1

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Answer 2

Given :

A piece of wire is bent in the form of an arc of a circle , of

length : 30 cm

angle subtended : 60°

Solution :

Here ,

A wire of 30 cm subtend an angle of 60° or π/3 at the center.

Now, if we have another wire long enough to form an entire circle , that circle will subtend an angle of 360° or 2π at the center .

so in the second case , the length of arc will be ,

                   30 cm  =  π/3

                     x cm   =  2π

Therefore, x = 180 cm

This is now the circumference of the circle ,

Therefore , 2πr = 180

                     or r = 90 / π

                          r = 28.6 cm (approx)

Final answer :

Hence, the radius of the circle is 90 / π or 28.6 cm .