Question

consider circle c with radius 5 cm and a central angle measure of 60°. what fraction of the whole circle is arc rs? 1/6 1/4 1/3 what is the approximate circumference of the circle? cm what is the approximate length of arc rs? cm

Explanation:

Step1: Recall circle - angle relationship

The total angle at the center of a circle is 360°.

Step2: Find the fraction of the arc

The central - angle of arc RS is 60°. The fraction of the whole circle that arc RS represents is $\frac{60}{360}=\frac{1}{6}$.

Step3: Calculate the circumference of the circle

The formula for the circumference of a circle is $C = 2\pi r$. Given $r = 5$ cm, $C=2\pi\times5 = 10\pi\approx10\times3.14 = 31.4$ cm.

Step4: Calculate the length of arc RS

The length of an arc $l$ is given by $l=\frac{\theta}{360}\times C$, where $\theta$ is the central - angle and $C$ is the circumference. Since $\theta = 60$ and $C\approx31.4$ cm, $l=\frac{60}{360}\times31.4=\frac{1}{6}\times31.4\approx5.23$ cm.

Answer:

What fraction of the whole circle is arc RS? $\frac{1}{6}$
What is the approximate circumference of the circle? $31.4$ cm
What is the approximate length of arc RS? $5.23$ cm