Question

find the length of the major arc. write your answer using \pi\ with no spaces.

\\(270^{\circ}\\)

\\(12\text{ m}\\)

\\(\text{length}_{\text{arc}} = \\) ______ \\(\text{m}\\)

Explanation:

Calculate the circumference of the circle

$$ C = 2 \pi r = 2 \pi (12) = 24\pi $$

Calculate the length of the major arc

$$ \text{Arc Length} = \frac{\theta}{360^\circ} \cdot C = \frac{270^\circ}{360^\circ} \cdot 24\pi = \frac{3}{4} \cdot 24\pi = 18\pi $$

Answer:

Find the length of the major arc. Write your answer using "pi" with no spaces.

Length\(_{\text{arc}}\) = <blank>18pi</blank> m