Question

the length of ab (the minor arc) is 20 cm. what is the circumference of ⊙c?
a. 120 cm
b. 720 cm
c. 200 cm
d. 72 cm
e. 56 cm
f. 360 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 $s=\frac{\theta}{360}\times2\pi r$, and the circumference $C = 2\pi r$. Let the circumference be $C$. We know that the arc - length $s = 20$ cm and $\theta=10^{\circ}$.

Step2: Set up proportion

Since $s=\frac{\theta}{360}\times C$, we can solve for $C$. Rearranging the formula gives $C=\frac{360\times s}{\theta}$.

Step3: Substitute values

Substitute $s = 20$ cm and $\theta = 10^{\circ}$ into the formula $C=\frac{360\times20}{10}$.
$C = 720$ cm.

Answer:

B. 720 cm