Questions: Find the arc-length of a circle with the given radius r and central angle θ. Give the answer in the given unit of measure, rounded to the nearest hundredth. r=58 m ; θ=240°

Solution Steps

To find the arc length \( L \) of a circle, we use the formula:

\[ L = \frac{\theta}{360} \times 2\pi r \]

Substituting the given values \( r = 58 \, \text{m} \) and \( \theta = 240^\circ \):

\[ L = \frac{240}{360} \times 2\pi \times 58 \]

Calculating the fraction:

\[ \frac{240}{360} = \frac{2}{3} \]

Thus, the arc length becomes:

\[ L = \frac{2}{3} \times 2\pi \times 58 \]

Calculating this gives:

\[ L \approx 242.94983187761065 \, \text{m} \]

Rounding the arc length to the nearest hundredth:

\[ L \approx 242.95 \, \text{m} \]

Final Answer