Question

In a circle with center C and radius 6, minor arc AB has a length of 4pi. What is the measure, in radians, of central angle ACB? PLZ EXPLAIN

A)2pi/9
B) pi/3
C)2pi/3
D)4pi/3

Answer 1

Short answer <<<< C
The length of an arc is given by the formula


`\text{Arc length =}(\theta)/(2\pi){2 \pi r}`

Since the arc length is given (4
`\pi`) and the radius is given (6), the central angle
`\theta` can be found

Arc Length = theta * r
4 pi = theta * 6 Divide by 6
4 pi / 6 = theta
theta = (2/3) pi <<<<<< answer.


Answer C <<<<<< answer.

Answer 2

To solve this problem, we need to know that
arc length = r &theta; where &theta; is the central angle in radians.

We're given
r = 6 (units)
length of minor arc AB = 4pi
so we need to calculate the central angle, &theta;
Rearrange equation at the beginning,
&theta; = (arc length) / r = 4pi / 6 = 2pi /3

Answer: the central angle is 2pi/3 radians, or (2pi/3)*(180/pi) degrees = 120 degrees