Question

A central angle measuring 120° intercepts an arc in a circle whose radius is 3.

What is length of the arc of the circle formed by this central angle? Round the length of the arc to the nearest hundredth of unit.

Answer 1

6.28

Explanation:

The length of arc which subtends an angle
`\alpha` at the center of a circle is given by
`\alpha r` where r is the radius of circle.

______________________________

given

the central angle of arc is 120°

`\pi = 180\\120 = (\pi /180)* 120\\120 = 2/3\pi`

we will use value of
`\pi` as 3.14

r = 3

Length of this arc is

`2/3( \pi *3) = 2\pi \\=2*3.14 = 6.28`

The length of the arc to the nearest hundredth of unit is 6.28