Question

set

1. circle a has a radius of 15 feet and a circumference of 30π feet or about 94.25 feet. segment cd is the

diameter of the circle.
a. what is the degree measure of arc cbd?
b. what is the length of arc cbd?
c. what is the ratio of the length of cbd to the length of the radius?

Explanation:

Step1: Determine the measure of arc \( CBD \)

Since \( CD \) is a diameter, the central angle \( \angle CAD = 180^{\circ} \). The measure of an arc is equal to the measure of its central angle. So, the degree measure of arc \( CBD \) is \( 180^{\circ} \).

Step2: Calculate the length of arc \( CBD \)

The formula for the length of an arc \( s=\frac{\theta}{360}\times 2\pi r \), where \( \theta \) is the central angle and \( r \) is the radius. Here, \( \theta = 180^{\circ} \) and \( r = 15\) feet.

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Step3: Find the ratio of the length of arc \( CBD \) to the radius

The length of arc \( CBD\approx47.1 \) feet and the radius \( r = 15\) feet. The ratio is \( \frac{47.1}{15}=3.14\approx\pi \)

Answer:

a. \( 180^{\circ} \)
b. \( 15\pi\approx47.1 \) feet
c. \( \pi\approx3.14 \)