Question

question 4 of 10
the length of ⁀xy (the minor arc) is 15 cm. what is the circumference of ⊙z?
a. 426 cm
b. 94.2 cm
c. 540 cm
d. 180 cm
e. 450 cm
f. 360 cm

Explanation:

Step1: Recall arc - length formula

The formula for the length of an arc $s$ is $s = r\theta$ (in radians) or $s=\frac{\theta}{360^{\circ}}\times C$ where $C$ is the circumference of the circle and $\theta$ is the central - angle in degrees. Here, $s = 15$ cm and $\theta=12^{\circ}$.

Step2: Rearrange the arc - length formula to find the circumference

We have $s=\frac{\theta}{360^{\circ}}\times C$. Rearranging for $C$, we get $C=\frac{360^{\circ}}{\theta}\times s$.

Step3: Substitute the given values

Substitute $\theta = 12^{\circ}$ and $s = 15$ cm into the formula $C=\frac{360^{\circ}}{12^{\circ}}\times15$ cm.
$C = 30\times15$ cm$=450$ cm.

Answer:

E. 450 cm