Answer:
The length of arc AC is [tex]15\pi\ cm[/tex]
Step-by-step explanation:
step 1
Find the circumference of the circle
The circumference is equal to
[tex]C=\pi D[/tex]
we have
[tex]D=36\ cm[/tex]
substitute
[tex]C=\pi (36)[/tex]
[tex]C=36\pi\ cm[/tex]
step 2
Find the length of arc AC
Remember that the circumference subtends a central angle of 360 degrees
The measure of arc AC is equal to
arc AC+30°=180° ----> because the diameter divide the circle into two equal parts
arc AC=180°-30°=150°
using proportion
[tex]\frac{36\pi}{360}=\frac{x}{150}\\ \\x=36\pi*150/360\\ \\x=15\pi\ cm[/tex]
