how long is the arc intersected by a central angle of $\frac{pi}{3}$ radians in a circle with a radius of 6…

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 $pi$.\n1.0 ft\n5.7 ft\n6.3 ft\n7.0 ft

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 $pi$.\n1.0 ft\n5.7 ft\n6.3 ft\n7.0 ft

Answer

Explanation:

Step1: Recall arc - length formula

The formula for the length of an arc $s$ of a circle is $s = r\theta$, where $r$ is the radius of the circle and $\theta$ is the central angle in radians.

Step2: Substitute given values

We are given that $r = 6$ ft and $\theta=\frac{\pi}{3}$ radians. Substituting these values into the formula, we get $s=6\times\frac{\pi}{3}$.

Step3: Simplify the expression

$6\times\frac{\pi}{3}=2\pi$.

Step4: Approximate the value

Since we are using $\pi = 3.14$, then $s = 2\times3.14=6.28$ ft.

Step5: Round to the nearest tenth

Rounding $6.28$ to the nearest tenth gives $6.3$ ft.

Answer:

C. 6.3 ft