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(\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(72^\circ )/(360^\circ)`

`44=6.28r(0.2)`

`44=1.256r`

Divide both sides by 1.256.

`(44)/(1.256)=r`

`35.031847=r`

`r=35.03`

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