Question

circle d has a radius of 3 centimeters.
what is the length of \\(\overarc{fg}\\)?
write an exact, simplified answer.
\\(\square\\) centimeters

Explanation:

Step1: Recall the arc length formula

The formula for the length of an arc \( s \) of a circle with radius \( r \) and central angle \( \theta \) (in degrees) is \( s=\frac{\theta}{360^{\circ}}\times2\pi r \).

Step2: Identify the values of \( r \) and \( \theta \)

Here, the radius \( r = 3 \) centimeters and the central angle \( \theta=110^{\circ} \).

Step3: Substitute the values into the formula

Substitute \( r = 3 \) and \( \theta = 110^{\circ} \) into the arc length formula:
\[

$$\begin{align*} s&=\frac{110^{\circ}}{360^{\circ}}\times2\pi\times3\\ &=\frac{110}{360}\times6\pi\\ &=\frac{110\times6\pi}{360}\\ &=\frac{660\pi}{360}\\ &=\frac{11\pi}{6} \end{align*}$$

\]

Answer:

\(\frac{11}{6}\pi\)