a circle has a radius of $3$. an arc in this circle has a central angle of $20^{\\circ}$.\n\nwhat is the…

a circle has a radius of $3$. an arc in this circle has a central angle of $20^{\\circ}$.\n\nwhat is the length of the arc?\neither enter an exact answer in terms of $\\pi$ or use $3.14$ for $\\pi$ and enter your answer as a decimal.

a circle has a radius of $3$. an arc in this circle has a central angle of $20^{\\circ}$.\n\nwhat is the length of the arc?\neither enter an exact answer in terms of $\\pi$ or use $3.14$ for $\\pi$ and enter your answer as a decimal.

Answer

Explanation:

Step1: Identify the arc length formula

The formula for the arc length $s$ of a circle with radius $r$ and central angle $\theta$ in degrees is: $$s = \frac{\theta}{360^\circ} \times 2\pi r$$

Step2: Substitute the given values

Substitute $r = 3$ and $\theta = 20^\circ$ into the formula: $$s = \frac{20^\circ}{360^\circ} \times 2\pi(3)$$

Step3: Simplify the expression

Simplify the fraction and the product: $$s = \frac{1}{18} \times 6\pi = \frac{6\pi}{18} = \frac{\pi}{3}$$

Step4: Calculate the decimal value

Using $\pi \approx 3.14$: $$s \approx \frac{3.14}{3} \approx 1.0466...$$

Answer:

$\frac{\pi}{3}$ or $1.05$