Answer:
Option D. [tex]\frac{9}{2}\pi \ ft[/tex]
Step-by-step explanation:
step 1
Find the circumference of the circle
The circumference of a circle is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=10\ ft[/tex]
substitute
[tex]C=2\pi (10)=20\pi\ ft[/tex]
step 2
we know that
360° subtends the complete circle of length 2πr.
so
By proportion
Find the length of the arc subtended by an angle measuring 81°
[tex]\frac{20\pi }{360}= \frac{x}{81}\\ \\x=20\pi (81)/360\\ \\x= \frac{9}{2}\pi \ ft[/tex]
