A circle has a radius of 3 . An arc in this circle has a central angle of $20^{\circ}$.
What is the length of the arc?
Either enter an exact answer in terms of $\pi$ or use 3.14 for $\pi$ and enter your answer as a decimal.
$\square$

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Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the arc length, we use the formula $s = r heta$ where $s$ is the arc length, $r$ is the radius, and $ heta$ is the central angle in radians. ‖ ‖ step 2 ⋮ Convert the central angle from degrees to radians. Since $180^\circ$ is equivalent to $\pi$ radians, $20^\circ$ is equivalent to $\frac{20}{180}\pi = \frac{\pi}{9}$ radians. ‖ ‖ step 3 ⋮ Substitute the radius $r = 3$ and the central angle $ heta = \frac{\pi}{9}$ radians into the arc length formula: $s = 3 \cdot \frac{\pi}{9}$. ‖ ‖ step 4 ⋮ Simplify the expression to find the arc length: $s = \frac{3\pi}{9} = \frac{\pi}{3}$. ‖ ∻Answer∻ ⚹ The length of the arc is $\frac{\pi}{3}$ or approximately 1.0472 when using $3.14$ for $\pi$. ⚹ ∻Key Concept∻ ⚹Arc Length in a Circle⚹ ∻Explanation∻ ⚹The arc length of a circle is calculated using the formula $s = r heta$, where the central angle $ heta$ must be in radians.⚹◊What formula can be used to calculate the length of an arc in a circle given the radius and central⍭ Generate me a similar question◊

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