Question

4. A circular wire of radius 15 cm is cut and wrapped round the circumference of a
wheel of radius 120 cm. Find the angle subtended by the wire at the centre of the
wheel.​

Answer 1

★Given:-

• Radius of circular wire = 15cm
• Radius of wheel = 120cm
• The circular wire is cut and wrapped round the circumference of wheel.

★To find:-

• The angle subtended by the wire at the centre of the  wheel.​

★Solution:-

We know:

✦Circumference of a circle = 2πr

Putting the values,

Circumference of wire:-

⇒ 2πr

⇒2×3.14×15

⇒ 94.2cm

Therefore,circumference of wire = 94.2cm

Given that the wire is cut and wrapped round the circumference of the wheel.

Therefore,the length of the arc is the circumference of the wire.

→ l = 94.2cm

Also, we know:

✦l = rθ

And we have,

• l = 94.2cm
• r = 120cm

Putting the values,

⇒ l = rθ

⇒ θ = l/r

⇒ θ = 94.2 / 120

      = 0.786radians

      = π/4

      = 45°

Hence,

The angle subtended by the wire at the center of the wheel is 45°.

_______________

Answer 2

Answer:

Correct Question:-

1. A circular wire of radius 15 cm is cut and bend so as to lie along the circumference of a hoop of radius 120 cm. The angle subtended by it at the centre is:

To find,

The angle that is subtended at the centre

Solution:-

C: = 2πr = 2 × π × 15 = 30π cm

12 (∅) = 30π

$∅= \frac{π}{4}= \frac{π}{4} ×180°$

= 45°

So the angle that is subtended at the centre is 45°