Question

3. A piece of wire is in the form of a
sector of a circle of radius 20 cm,
subtending an angle 150° at the centre.
If it is bent in the form of a circle, then
what will be its radius?
22
(a)
19
3
cm
(b) 7 cm.
( 8 cm
(d) None of the above​

Answer 1

Given :-

◉ A piece of wire is in the form of a sector of a circle of radius r = 20 cm , subtending an angle θ = 150°

To Find :-

◉ Radius of the circle which is formed by bending the wire.

Solution :-

Since, the angle θ, between the two radii of the circle is 150°.

We know, Length of a sector subtending an angle θ at the center of the circle is:

⇒ 2πr θ/360°

∴ Length of wire = 2×π×r×150/360

⇒ Length = 2×π×20×5/12

⇒ Length = 50π/3 cm ...(1)

Now, It is given in the question that the wire is bent to form a circle.

∴ Length of Wire = Circumference of circle

⇒ 2πr₁ = 50π/3

⇒ 2×r₁ = 50/3

⇒ r₁ = 25/3

Hence, The radius of the circle formed by bending the wire is 25/3 cm

Since, The answer 25/3 is not given in the options, Hence Option (D) - None of the above is the correct option.