Question

the length of ⌢de (the minor arc) is 22 cm. what is the circumference of ⊙f? a. 660 cm b. 138.16 cm c. 528 cm d. 220 cm e. 330 cm f. 1036.2 cm

Explanation:

Step1: Recall arc - length formula

The formula for the length of an arc $s$ is $s=\frac{n}{360}\times C$, where $n$ is the central - angle measure in degrees and $C$ is the circumference of the circle. We know that $s = 22$ cm and $n = 15^{\circ}$.

Step2: Solve for the circumference $C$

From $s=\frac{n}{360}\times C$, we can re - arrange it to get $C=\frac{360\times s}{n}$. Substitute $s = 22$ cm and $n = 15^{\circ}$ into the formula: $C=\frac{360\times22}{15}$.

Step3: Calculate the value of $C$

First, calculate $360\times22 = 7920$. Then, divide by 15: $\frac{7920}{15}=528$ cm.

Answer:

C. 528 cm