Question:
In a circle with a radius of 5, what is the length of an arc that subtends a central angle of 120 degrees?
In a circle with a radius of 5, what is the length of an arc that subtends a central angle of 120 degrees?
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To find the length of an arc, use the formula \( L = \frac{\theta}{360^\circ} \times 2\pi r \), where \( \theta \) is the central angle and \( r \) is the radius of the circle.
Updated On: Oct 6, 2025
- \( \frac{5\pi}{3} \)
- \( \frac{10\pi}{3} \)
- \( 5\pi \)
- \( 10\pi \)
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The Correct Option is B
Solution and Explanation
The formula for the length \( L \) of an arc is given by:
\[
L = \frac{\theta}{360^\circ} \times 2\pi r,
\]
where \( \theta \) is the central angle and \( r \) is the radius.
Step 1: Substitute the known values \( \theta = 120^\circ \) and \( r = 5 \) into the formula:
\[
L = \frac{120^\circ}{360^\circ} \times 2\pi \times 5.
\]
Step 2: Simplify:
\[
L = \frac{1}{3} \times 2\pi \times 5 = \frac{10\pi}{3}.
\]
Thus, the length of the arc is \( \frac{10\pi}{3} \).
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