In order to fully understand Arc Length and Area in Calculus, you first have to know where all of it comes from. And that’s what this lesson is all about!
Arc Length, according to Math Open Reference, is the measure of the distance along a curved line.
In other words, it’s the distance from one point on the edge of a circle to another, or just a portion of the circumference.
So how do we calculate this, since we only know how to find distances for straight lines, not curves?
Well, it all comes down to radians and proportions!
What we discover is that the length of an arc of a circle is proportional to the measure of it’s central angle.
Arc Length Formula
All this means is that by the power of radians and proportions, the length of an arc is nothing more than the radius times the central angle!
Easy!
We will use our new found skills of finding arc length to see how one wheel can turn another, as well as how many inches a pulley can lift a weight.
Additionally, we will see how right triangles and fractions can help us find the Area of a Sector, which, according to Cool Math, is the area between two segments coming out of the center of a circle.
Ok, all this means is that a sector is just a fancy way of saying a portion of a circle (i.e., slice of pizza or a slice of pie).
I’m already hungry!
Again, we will use our new found formula and apply it to several problems where we are asked to find area.
These two concepts are going to be so helpful when we get to calculus, and are asked to find the arc length and area of things other than circles. Because, we will be armed with the power of circles, triangles, and radians, and will see how to use our skills and tools to some pretty amazing math problems. I can’t wait!
Arc Length – Worksheet
- Arc Length Example Problems: This handout contains 7 examples on finding arc length given radius and central angles.
Finding Arc Length – Video
Get access to all the courses and over 450 HD videos with your subscription
Monthly and Yearly Plans Available
Still wondering if CalcWorkshop is right for you?
Take a Tour and find out how a membership can take the struggle out of learning math.