Find the length to three significant digits of each arc intercept...

Question

Find the length to three significant digits of each arc intercepted by a central angle  in a circle of radius r. See Example 1.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          r = 12.3 cm , θ = 2π/3 radians

Accepted Answer

Hello, today we're going to be determining the arc length with a given central angle and the radius of the circle. Then we'll be expressing our answer to two decimal places. So what we currently have is we have a circle. This circle has a central angle in it data. Now the central angle that is given to us is the is equal to three pi divided by four radiant. So the central angle theta is given to us in terms of radiance. We are also told that the radius of the circle is 23.9 millimeters. We need to use this information to determine the length of the arc that is formed by the central angle. So how can we do this? Well, we do have an equation that helps us calculate the central angle or the arc length of a circle. The arc length of a circle is given to us as S is equal to R multiplied by theta. This is where R represents the radius of the circle and theta represents the central angle in terms of radiance. Now, our central angle theta is already given to us in terms of radiance. And we have the radius of a circle. So we have all the information, we need to calculate the arc length of the circle. So if we plug in the given information, we have ss equal to the radius which is 23. millimeters multiplied by the central angle which is three pi divided by four, 23.9 multiplied by three pi divided by four will give us the value of 71.7 pi divided by four millimeters. Now, at this point, I would recommend plugging in this value into a calculator. When doing so, you'll end up with a very lengthy decimal. This value will approximately equal to 56.313048 and continuing millimeters. Now, at this point, we're going to round this decimal to two decimal places. That means we're going to be taking a look at the number to the right of one. This number is less than five. So we're going to be keeping the one as it is. And with that being said, the final arc length for the circle is 56. millimeters. This will be the answer to our question. And with that being said, the overall answer is going to be D. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

Find the length to three significant digits of each arc intercepted by a central angle in a circle of radius r. See Example 1. r = 12.3 cm , θ = 2π/3 radians

Key Concepts

Arc Length Formula

Central Angle

Significant Figures

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