Question

how long is the arc intersected by a central angle of \\(\frac{\pi}{3}\\) radians in a circle with a radius of 6 ft? round your answer to the nearest tenth. use 3.14 for \\(\pi\\).\
\\(\bigcirc\\) 1.0 ft\
\\(\bigcirc\\) 5.7 ft\
\\(\bigcirc\\) 6.3 ft\
\\(\bigcirc\\) 7.0 ft

Explanation:

Step1: Recall arc length formula

The formula for the length of an arc \( s \) when the central angle \( \theta \) is in radians is \( s = r\theta \), where \( r \) is the radius of the circle.

Step2: Substitute values

Given \( r = 6 \) ft and \( \theta=\frac{\pi}{3} \) radians. Substitute these into the formula: \( s = 6\times\frac{\pi}{3} \). Simplify \( 6\times\frac{\pi}{3}=2\pi \).

Step3: Use \( \pi = 3.14 \)

Now, substitute \( \pi = 3.14 \) into \( 2\pi \): \( 2\times3.14 = 6.28 \).

Step4: Round to nearest tenth

Rounding \( 6.28 \) to the nearest tenth gives \( 6.3 \).

Answer:

6.3 ft (corresponding to the option "6.3 ft")