Question

the circumference of ⊙c is 56 cm. what is the length of ab⏜ (the minor arc)?

Explanation:

Step1: Recall arc - length formula

The length of an arc of a circle is given by the formula $s=\frac{\theta}{360^{\circ}}\times C$, where $\theta$ is the central - angle of the arc and $C$ is the circumference of the circle.

Step2: Identify values

The central - angle of the minor arc $\overset{\frown}{AB}$ is $\theta = 90^{\circ}$, and the circumference $C = 56$ cm.

Step3: Calculate arc length

Substitute $\theta = 90^{\circ}$ and $C = 56$ cm into the formula: $s=\frac{90^{\circ}}{360^{\circ}}\times56=\frac{1}{4}\times56 = 14$ cm.

Answer:

D. 14 cm