Question

in circle l, (overset{\frown}{nop}) is 90° and the radius is 5 units. which statement best describes the length of (overset{\frown}{nop})? (\frac{1}{4}) the area of circle l (\frac{1}{4}) the circumference of circle l (\frac{1}{2}) the area of circle l (\frac{1}{2}) the circumference of circle l

Explanation:

Step1: Recall arc - length formula

The length of an arc $s$ of a circle with radius $r$ and central - angle $\theta$ (in degrees) is given by $s=\frac{\theta}{360}\times2\pi r$. The area of a circle is $A = \pi r^{2}$.

Step2: Identify the central - angle of arc NOP

The central - angle of arc $\overset{\frown}{NOP}$ is $\theta = 90^{\circ}$, and the radius of the circle $r = 5$ units.

Step3: Calculate the fraction of the circle's circumference that the arc represents

Using the arc - length formula $s=\frac{\theta}{360}\times2\pi r$, substituting $\theta = 90^{\circ}$ into the formula, we get $s=\frac{90}{360}\times2\pi r=\frac{1}{4}\times2\pi r$. The circumference of a circle is $C = 2\pi r$. So the length of arc $\overset{\frown}{NOP}$ is $\frac{1}{4}$ of the circumference of circle $L$.

Answer:

B. $\frac{1}{4}$ the circumference of circle L