Question

A circle has a radius of 5 inches. Find the length of the arc intercepted by a central angle of 300 degrees. Round to the nearest hundredth of an inch.A circle has a radius of 5 inches. Find the length of the arc intercepted by a central angle of 300 degrees. Round to the nearest hundredth of an inch.choice:13.01 inches8.33 inches26.18 inches9.424.78 inches

Answer 1

ANSWER:

3rd option: 26.18 inches

STEP-BY-STEP EXPLANATION:

The length of the arc is calculated by a proportion between the circumference, which is the measure of the 360° of the circle, and the length of the 300°.

Therefore, the first thing is to calculate the circumference just like this:

$\begin{gathered} c=2\pi r \\ \\ \text{ We replacing} \\ \\ c=(2)(3.14)(5) \\ \\ c=31.415\text{ in} \end{gathered}$

Now, if we calculate the length of the arc using the proportion, like this:

$\begin{gathered} \:\frac{31.415}{360}=\frac{arc}{300}\: \\ \\ arc=31.415\cdot\frac{300}{360} \\ \\ arc=26.18\text{ in} \end{gathered}$

Therefore, the correct answer is 3rd option: 26.18 inches