Question

what angle does an arc 6.6cm on length subtends at the centre of a circle of radius 14cm? take
$\pi = 22 \7$​

Answer 1

Given:

Arc length = 6.6 cm

Radius = 14 cm

To find:

The angle subtended by the arc at the center.

Solution:

The formula for arc length is:

$s=2\pi r\dfrac{\theta}{360}$

Where, s is the arc length, r is the radius and $\theta$ is the central angle in degrees.

Putting $s=6.6,\pi=\dfrac{22}{7},r=14$,we get

$6.6=2\times \dfrac{22}{7}\times 14\times \dfrac{\theta}{360}$

$6.6=88\times \dfrac{\theta}{360}$

$\dfrac{6.6}{88}\times 360=\theta$

$27^\circ=\theta$

Therefore, the measure of the central angle is $27^\circ$.