Question

A)If a circle has a radius of 103 meters and a central angle of π3, then what is the length of the minor arc created by that angle to the nearest whole meter?(1 point)
Responses

108 m
108 m

103 m
103 m

97 m
97 m

98 m
98 m

Answer 1

To find the length of the minor arc created by a central angle, you can use the formula:

\[
\text{Arc Length} = r \cdot \theta
\]

where \( r \) is the radius of the circle and \( \theta \) is the central angle in radians.

Given:
- Radius \( r = 103 \) meters
- Central angle \( \theta = \frac{\pi}{3} \) radians

Now, substituting the values into the formula:

\[
\text{Arc Length} = 103 \cdot \frac{\pi}{3}
\]

Calculating this:

\[
\text{Arc Length} \approx 103 \cdot 1.0472 \approx 107.8 \text{ meters}
\]

Rounding to the nearest whole meter gives us 108 meters.

Thus, the length of the minor arc is approximately **108 m**.