Question

In a circle with a radius of 5 cm, what is the length of the arc subtended by a central angle of 120 degrees?​

Answer 1

Explanation:

The length of an arc in a circle is given by the formula:

`( \text{Arc Length} = \frac{\text{Central Angle}}{360} * 2\pi * \text{Radius} ).`

In this case, with a central angle of 120 degrees and a radius of 5 cm:

Arc Length =
`((120)/(360) * 2\pi * 5) cm.`

Calculating this gives an arc length of approximately 10.47 cm.

Answer 2

length of arc ≈ 10.5 cm

Explanation:

the arc length is calculated as

arc = circumference of circle × fraction of circle

= 2πr ×
`(120)/(360)` ( r is the radius )

= 2π × 5 ×
`(1)/(3)`

= 10π ×
`(1)/(3)`

=
`(10)/(3)` × π

≈ 10.5 cm ( to the nearest tenth )