Question

For a circle with a diameter of 6 meters, what is the measurement of a central angle (in degrees) subtended by an arc with a length of 7 3 π meters?

Answer 1

Answer : The measurement of a central angle is,
`140^o`

Step-by-step explanation :

Formula used for angle subtended by an arc is:

`s=(\pi r\theta)/(180)`

where,

s = arc length =
`(7)/(3)\pi m`

r = radius =
`(diameter)/(2)=(6m)/(2)=3m`

Now put all the given values in the above formula, we get:

`s=(\pi r\theta)/(180)`

`(7)/(3)\pi=(\pi * (3)* \theta)/(180)`

`\theta =140^o`

Thus, the measurement of a central angle is,
`140^o`