Question

consider circle c with radius 5 cm and a central angle measure of 60°. what fraction of the whole circle is arc rs? what is the approximate circumference of the circle? cm what is the approximate length of arc rs? cm 2.6 5.2 13.1

Explanation:

Step1: Find the fraction of arc RS

The fraction of a circle that an arc represents is given by the ratio of the central angle of the arc to the total central angle of a circle ($360^{\circ}$).
The central angle for arc RS is $60^{\circ}$. So the fraction is $\frac{60}{360}=\frac{1}{6}$.

Step2: Calculate the circumference of the circle

The formula for the circumference of a circle is $C = 2\pi r$. Given $r = 5$ cm, $C=2\times\pi\times5\approx2\times3.14\times5 = 31.4$ cm.

Step3: Calculate the length of arc RS

The formula for the length of an arc is $L=\frac{\theta}{360}\times2\pi r$ (where $\theta$ is the central angle). Substituting $\theta = 60^{\circ}$ and $r = 5$ cm, $L=\frac{60}{360}\times2\times3.14\times5=\frac{1}{6}\times31.4\approx5.2$ cm.

Answer:

• Fraction of arc RS: $\frac{1}{6}$
• Circumference of the circle: $31.4$ cm
• Length of arc RS: $5.2$ cm