Question

the radius of a circle is 4 feet. what is the length of a 90° arc?
90°
r=4 ft
give the exact answer in simplest form.
feet
π
□/□
submit

Explanation:

Step1: Recall arc length formula

The formula for the length of an arc is $L = \frac{\theta}{360^\circ} \times 2\pi r$, where $\theta$ is the central angle in degrees and $r$ is the radius of the circle.

Step2: Identify given values

Here, $\theta = 90^\circ$ and $r = 4$ feet. Substitute these values into the formula.
$L = \frac{90^\circ}{360^\circ} \times 2\pi \times 4$

Step3: Simplify the expression

Simplify $\frac{90^\circ}{360^\circ}=\frac{1}{4}$. Then, $L = \frac{1}{4} \times 8\pi$. Further simplifying, $L = 2\pi$.

Answer:

$2\pi$