The length of an arc of a circle is one-eighth the circumference of the circle.Find the angle subtended by this arc at the centre if the radius of the circle is 14cm

Question

asked Apr 21, 2022 122k views

1 Answer

Bernard Moeskops · Answer 1 · 2022-04-27T05:08:32+0000

Given:

The radius of the circle is 14 cm.

The length of an arc of a circle is one-eighth the circumference of the circle.

To find:

The angle subtended by this arc at the center.

Solution:

Formula for arc length is:

$s=2\pi r* (\theta )/(360^\circ)$ ...(i)

Where, r is the radius and
$\theta$ is the central angle.

The length of an arc of a circle is one-eighth the circumference of the circle.

$s=(1)/(8)(2\pi r)$ ...(ii)

Where,
$2\pi r$ is the circumference of the circle.

Using (i) and (ii), we get

$2\pi r* (\theta )/(360^\circ)=(1)/(8)(2\pi r)$

$(\theta )/(360^\circ)=(1)/(8)$

$\theta =(360^\circ)/(8)$

$\theta =45^\circ$

Therefore, the central angle is 45 degrees.