Question

Please help me

Please show all your work and round it your answer as needed.

1. Find the length of AB. Round it to the nearest hundredth.

Answer 1

Given that the radius of the circle is 6 cm.

The central angle is 120°

We need to determine the length of AB.

Length of AB:

The length of AB can be determined using the formula,

`{arc \ length}=2 \pi r\left((\theta)/(360)\right)`

where
`\theta` is the central angle and r is the radius of the circle.

Substituting
`\theta=120` and
`r=6` in the above formula, we get;

`arc\ length}=2 \pi (6)\left((120)/(360)\right)`

Simplifying the values, we get;

`arc\ length}=2 \pi (6)\left((1)/(3)\right)`

`arc\ length}=12 \pi \left((1)/(3)\right)`

`arc\ length}=4 \pi`

Substituting π = 3.14, we have;

`arc\ length}=4(3.14)`

`arc\ length}=12.56`

Thus, the arc length of AB is 12.56 cm