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Circle B below has a radius of 4 and arc AC has a central degree measure of 145°. What is the approximate length of arc AC?
Title
Length of arc AC
Your Result
Correct
Difficulty
Hard
Your Pace
0:02
Others' Pace
1:20
Video Explanation
Text Explanation
The answer is B. An arc is a fraction of the circumference of a circle. We can find the length of the arc by setting up a proportion using the ratio of the central degree angle to the total degrees in a circle and the ratio of the arc length to the circumference of the circle.
As long as we know (or can find) the radius, we can find the circumference of the circle.
The circumference of this circle then is 2π x 4 or 8π.
We can set up the following proportion to determine the length of the arc:
By cross-multiplying, we get
x is closest to , so
our answer is B.
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