Question

Arc CD is Two-thirds of the circumference of a circle. What is the radian measure of the central angle? StartFraction 2 pi Over 3 EndFraction radians StartFraction 3 pi Over 4 EndFraction radians StartFraction 4 pi Over 3 EndFraction radians StartFraction 3 pi Over 2 EndFraction radians CAN YOU SHOW WORK PLEASE

Answer 1

The answer is C on Edge 2020

Explanation:

I did the assignment

Answer 2

`\theta = (4\pi)/(3)`

Explanation:

Given

Let A represent the Length of Arc CD and C, represents the circumference

`A = (2)/(3) C`

Required

Find the central angle (in radians)

The length of arc CD in radians is as follows;

`A = r\theta`

Where r is the radius and
`\theta` is the measure of central angle

The circumference of a circle is calculated as thus;

`C = 2\pi r`

From the question, it was stated that the arc length is 2-3rd of the circumference;

This means that

`A = (2)/(3) C`

Substitute
`2\pi r` for C and
`r\theta` for A

`A = (2)/(3) C` becomes

`r\theta = (2)/(3) * 2\pi r`

`r\theta = (4\pi r)/(3)`

Divide both sides by r

`(r\theta)/(r) = (4\pi r)/(3)/r`

`(r\theta)/(r) = (4\pi r)/(3) * (1)/(r)`

`\theta = (4\pi r)/(3) * (1)/(r)`

`\theta = (4\pi)/(3)`

Hence, the measure of the central angle;
`\theta = (4\pi)/(3)`