Question

consider circle c with radius 5 cm and a central - angle measure of 90°. 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? 15.7 31.4 78.5 cm

Explanation:

Step1: Find fraction of arc

The measure of a full - circle is 360°. The central angle of arc $RS$ is 90°. The fraction of the whole circle that arc $RS$ is $\frac{\text{central angle of arc }RS}{360^{\circ}}$.
$\frac{90^{\circ}}{360^{\circ}}=\frac{1}{4}$

Step2: Calculate circumference

The formula for the circumference of a circle is $C = 2\pi r$. Given $r = 5$ cm, then $C=2\pi\times5 = 10\pi\approx10\times 3.14 = 31.4$ cm.

Step3: Calculate arc length

The length of an arc $s$ is given by $s=\text{fraction of circle}\times C$. Since the fraction of the circle for arc $RS$ is $\frac{1}{4}$ and $C\approx31.4$ cm, then $s=\frac{1}{4}\times31.4 = 7.85$ cm.

Answer:

Fraction of the whole circle that arc $RS$ is: $\frac{1}{4}$
Approximate circumference of the circle: $31.4$ cm
Approximate length of arc $RS$: $7.85$ cm