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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.
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