Question

enter as an exact answer in terms of π, or as a decimal rounded to the hundredths place. a circle with radius 30 has an arc with a 90° 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 $r = 30$ and $\theta=90^{\circ}$.
Substitute into the formula: $L=\frac{90}{360}\times2\pi\times30$.

Step3: Simplify the expression

First, $\frac{90}{360}=\frac{1}{4}$. Then $L=\frac{1}{4}\times2\pi\times30$.
$\frac{1}{4}\times2\pi\times30=\frac{1\times2\pi\times30}{4}=\frac{60\pi}{4}=15\pi$.
If we calculate the decimal value, since $\pi\approx3.14$, then $L = 15\times3.14=47.12$.

Answer:

$15\pi$ or $47.12$