Question

enter as an exact answer in terms of π, or as a decimal rounded to the hundredths place. a circle with radius 468 has an arc with a 10° angle. what is the length of the arc? show your work here hint: to add the pi symbol (π), type \pi\

Explanation:

Step1: Recall the arc - length formula

The formula for the length of an arc is $L=\frac{\theta}{360}\times2\pi r$, where $\theta$ is the central angle in degrees and $r$ is the radius of the circle.

Step2: Substitute the given values

Given that $r = 468$ and $\theta=10^{\circ}$.
Substitute into the formula: $L=\frac{10}{360}\times2\pi\times468$.
First, simplify $\frac{10}{360}=\frac{1}{36}$.
Then $L=\frac{1}{36}\times2\pi\times468$.
$2\times468 = 936$, so $L=\frac{936}{36}\pi$.
Since $\frac{936}{36}=26$, $L = 26\pi$.
If we calculate the decimal value, using $\pi\approx3.14$, then $L=26\times3.14=81.64\approx81.68$.

Answer:

$\frac{26}{1}\pi$ or $81.68$