Question

the radius of a circle is 3 feet. what is the length of a 90° arc?
give the exact answer in simplest form.
feet

Explanation:

Step1: Recall the arc length formula

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

Step2: Substitute the given values

We know that \( \theta = 90^\circ \) and \( r = 3 \) feet. Substituting these values into the formula, we get \( L=\frac{90^\circ}{360^\circ}\times2\pi\times3 \).

Step3: Simplify the expression

First, simplify \( \frac{90^\circ}{360^\circ}=\frac{1}{4} \). Then, calculate \( 2\pi\times3 = 6\pi \). Now, multiply \( \frac{1}{4} \) and \( 6\pi \): \( \frac{1}{4}\times6\pi=\frac{6\pi}{4}=\frac{3\pi}{2} \).

Answer:

\( \frac{3\pi}{2} \)