Question

39. Find the length of each arc shown in red. Leave your answer in simplified radical form.

Answer 1

Answer:

The length of the arc shown in red is $\frac{22}{9}\pi\ in$

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference is equal to

$C=2\pi r$

we have

$r=4\ in$

substitute

$C=2\pi (4)$

$C=8\pi\ in$

step 2

Find the length of the arc in red

Remember that the length of the circumference subtends a central angle of 360 degrees

so

by proportion find the length of the arc by a central angle of 110 degrees

$\frac{8\pi}{360}=\frac{x}{110}\\ \\x=8\pi*110/360\\ \\x=\frac{880}{360}\pi\ in$

Simplify

$\frac{880}{360}\pi=\frac{22}{9}\pi\ in$