Geometry Teachers Never Spend Time Trying to Find Materials for Your Lessons Again!
Join Our Geometry Teacher Community Today!
How do you use the arc length of a circle to find the diameter of a circle?
We will look at some application problems using sector area and arc length
A pie is cut into 6 equal pieces. The arc length of one piece of pie is 5.4 cm. What is the diameter of the pie?
So our strategy is to always draw a picture.
Let's start by drawing a picture of the pie and assume it is a circular pie. Let's draw 6 equal pieces. If we have 360 degrees divided by into 6 pieces our central angle is going to be 60 degrees. This gives you an idea of what we are working with. What we will do is use a " Proportion Method" to find the circumference, and then use the circumference to calculate diameter.
The proportion method it works like this. We take the arc length and put it over the circumference and set it equal to measure of the angle over 360 degrees. So let's plug in what we know. The arc length equals is 5.4 and we don't know circumference which will become x, and angle measure equals 60 degrees.
We then cross product1 times x and 6 times 5= 32.4 which equals my circumference.
Next we can work backwards to find the diameter.
Circumference = Diameter times Pi which is 32.4. So I will take 32.4 and divide it by Pi and I get 10.31
The pie's diameter is 10.31 centimeters.
That is how you use the arc length to find diameter of a circle.
You may also enjoy...
Circles Radius Diameter & Pi Math Learning Upgrade
Diameter of a Circle Calculate diameter given circumference
Please watch: "Study Skills Teacher's Secret Guide to your Best Grades"
Tagged under: Geomery,Circle,Arc length,Diameter,Using arc length find diameter,Geometry (Field Of Study)
Clip makes it super easy to turn any public video into a formative assessment activity in your classroom.
Add multiple choice quizzes, questions and browse hundreds of approved, video lesson ideas for Clip
Make YouTube one of your teaching aids - Works perfectly with lesson micro-teaching plans
1. Students enter a simple code
2. You play the video
3. The students comment
4. You review and reflect
* Whiteboard required for teacher-paced activities
With four apps, each designed around existing classroom activities, Spiral gives you the power to do formative assessment with anything you teach.
Carry out a quickfire formative assessment to see what the whole class is thinking
Create interactive presentations to spark creativity in class
Student teams can create and share collaborative presentations from linked devices
Turn any public video into a live chat with questions and quizzes