Question

question 1 of 10
in the diagram below, what is the approximate length of the minor arc (widehat{xy})?
a. 7.1 cm
b. 5.7 cm
c. 6.3 cm
d. 3.1 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 $s=\frac{\theta}{360}\times2\pi r$.

Step2: Identify values of $\theta$ and $r$

Here, $\theta = 40^{\circ}$ and $r = 9$ cm.

Step3: Substitute values into the formula

$s=\frac{40}{360}\times2\pi\times9$.
First, simplify $\frac{40}{360}=\frac{1}{9}$. Then, $s=\frac{1}{9}\times2\pi\times9$.
The 9s cancel out, and we get $s = 2\pi\approx2\times3.14 = 6.28\approx6.3$ cm.

Answer:

C. 6.3 cm