Question

how long is the arc intersected by a central angle of π/3 radians in a circle with a radius of 6 feet round your answer to the nearest tenth

Answer 1

$\bf \textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ \cline{1-1} r=6\\ \theta =\frac{\pi }{3} \end{cases}\implies s=6\left( \frac{\pi }{3} \right)\implies s=2\pi \implies \stackrel{\textit{rounded up}}{s=6.3}$

Answer 2

Answer: $arc\ length=6.3\ ft$

Step-by-step explanation:

You  need to use the following formula for calculate the arc lenght:

$arc\ length=r\theta$

Where  "r" is the radius and $\theta$ is the central angle in radians.

You know that the central angle in radians s:

$\theta=\frac{\pi }{3}$

And the radius is:

$r=6\ ft$

Therefore, the final step is to substitute the values into the formula. Then you get:

$arc\ length=(6\ ft)(\frac{\pi }{3})$

$arc\ length=6.3\ ft$