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
\frac{□}{□}

Explanation:

Step1: Recall arc length formula

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

Step2: Substitute values

Here, \( \theta = 90^\circ \) and \( r = 4 \) feet. Substitute these values into the formula:
\( s=\frac{90^\circ}{360^\circ}\times2\pi\times4 \)

Step3: Simplify the expression

First, simplify \( \frac{90^\circ}{360^\circ}=\frac{1}{4} \). Then, calculate \( 2\pi\times4 = 8\pi \). Now, multiply by \( \frac{1}{4} \):
\( s=\frac{1}{4}\times8\pi = 2\pi \)

Answer:

\( 2\pi \)