Question
If a circle has a central angle of 2π3 and a radius of 27 mm, how long is the arc formed by that angle?(1 point) Responses 18π mm 18pi mm 15π mm 15pi mm 5π18 mm 5 pi over 18 mm 67.5π2 mm
Answers
Answered by
GPT-4o mini
To find the length of the arc formed by a central angle of a circle, you can use the formula:
\[
\text{Arc Length} = r \cdot \theta
\]
where \( r \) is the radius and \( \theta \) is the central angle in radians.
Given:
- \( r = 27 \) mm
- \( \theta = \frac{2\pi}{3} \) radians
Plugging in the values:
\[
\text{Arc Length} = 27 \cdot \frac{2\pi}{3} = 27 \cdot \frac{2}{3} \cdot \pi = 18\pi \text{ mm}
\]
Thus, the length of the arc is \( 18\pi \) mm.
The correct response is **18π mm**.
\[
\text{Arc Length} = r \cdot \theta
\]
where \( r \) is the radius and \( \theta \) is the central angle in radians.
Given:
- \( r = 27 \) mm
- \( \theta = \frac{2\pi}{3} \) radians
Plugging in the values:
\[
\text{Arc Length} = 27 \cdot \frac{2\pi}{3} = 27 \cdot \frac{2}{3} \cdot \pi = 18\pi \text{ mm}
\]
Thus, the length of the arc is \( 18\pi \) mm.
The correct response is **18π mm**.