Question

question 11 (multiple choice worth 1 points) (07.03 mc) in circle l, (overarc{op}) is (45^circ) and the radius is 5 units. which statement best describes the length of (overarc{op})? (\bigcirc \frac{1}{8}) the circumference of circle l (\bigcirc \frac{1}{8}) the area of circle l (\bigcirc \frac{1}{2}) the circumference of circle l (\bigcirc \frac{1}{2}) the area of circle l

Explanation:

Step1: Recall arc length formula

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

Step2: Identify given values

Here, \( \theta = 45^{\circ} \) and \( r = 5 \) units. The circumference of a circle is \( C = 2\pi r \).

Step3: Substitute into arc length formula

Substitute \( \theta = 45^{\circ} \) into the arc length formula: \( s=\frac{45^{\circ}}{360^{\circ}}\times C \). Simplify \( \frac{45}{360}=\frac{1}{8} \). So the arc length \( \overset{\frown}{OP} \) is \( \frac{1}{8} \) of the circumference of circle \( L \).

Answer:

\( \frac{1}{8} \) the circumference of circle \( L \) (the first option among the choices, likely labeled as the option with \( \frac{1}{8} \) and "the circumference of circle \( L \)")