Question

question 10 of 10
in the diagram below, what is the approximate length of the minor arc $widehat{de}$?
a. 11.8 cm
b. 19.7 cm
c. 23.6 cm
d. 47.1 cm

Explanation:

Step1: Recall arc - length formula

The formula for the length of an arc $s$ of a circle is $s = r\theta$, where $r$ is the radius of the circle and $\theta$ is the central - angle in radians.

Step2: Convert the angle from degrees to radians

We know that $90^{\circ}=\frac{\pi}{2}$ radians, and the radius $r = 15$ cm.

Step3: Calculate the arc - length

Substitute $r = 15$ cm and $\theta=\frac{\pi}{2}$ into the arc - length formula: $s=15\times\frac{\pi}{2}$.
Using $\pi\approx3.14$, we have $s = 15\times\frac{3.14}{2}=23.55\approx23.6$ cm.

Answer:

C. 23.6 cm