Question

the length of (widehat{xy}) (the minor arc) is 48 cm. what is the circumference of (odot z)? a. 384 cm b. 192 cm c. 288 cm d. 24 cm e. 326 cm f. 301.44 cm

Explanation:

Step1: Recall arc - length formula

The formula for the length of an arc $s$ of a circle with radius $r$ and central - angle $\theta$ (in degrees) is $s=\frac{\theta}{360}\times C$, where $C$ is the circumference of the circle. Here, $\theta = 60^{\circ}$ and $s = 48$ cm.

Step2: Rearrange the formula to solve for $C$

We have $48=\frac{60}{360}\times C$. Rearranging for $C$, we get $C=\frac{48\times360}{60}$.

Step3: Calculate the circumference

$C = 288$ cm.

Answer:

C. 288 cm