Question

The arc made by a sector at center is 72 degrees . Given that the length of an arc is 44cm ,calculate the radius of the circle (Take pi as 3.14)

Answer 1

Given:

Central angle of a sector = 72 degrees

Intercepted arc length = 44 cm

To find:

The radius of the circle.

Solution:

We know that, the arc length is

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

Where, r is the radius of the circle, $\theta$ is the central angle in degrees.

Putting $s=44,\pi=3.14$ and $\theta = 72^\circ$, we get

$44=2(3.14)r\dfrac{72^\circ }{360^\circ}$

$44=6.28r(0.2)$

$44=1.256r$

Divide both sides by 1.256.

$\dfrac{44}{1.256}=r$

$35.031847=r$

$r=35.03$

Therefore, the radius of the circle is about 35.03 cm.