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In this video you will learn an alternative method for finding the area of a circle.
You can use the sector area in order to find the area of the entire circle.
In the last lesson I should you a proportion method, and we are going to use that same method to get the area of the circle.
Find the area of a circle, given the area of the sector.
I need to zoom out, there you go.
What I will do is take my sector area, which is my slice of pizza and set that equal to my measure of the arc xz over the area 360, because that the degree measure of the whole circle.
Now lets plug in some of the things we do know. The sector area is 95 cm.
We don't know the area of a circle, this is what we need to find. Lets call that X, which will be equal to the measure of the arc.
What is the measure of the arc? It is 150 degrees over 360 degrees.
Once we get proportions is is really easy, we just complete cross products. I like to reduce before I complete a cross product just to make my numbers smaller, but you don't have to. I will divide by 10. Next I will divide by 3. Ths reduces to 5/12. Now my cross product is a little easier
5 times x is 5x.
Grad my calculator 12 times 95 = 1140
Next divide by 5 = 228
This means the area of the circle equals 228cm for the whole circle using the proportion method.
You can use the formula, but I find the proportion method easier.
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Tagged under: geometry,area,area circle,moomoomath,math,finding area circle
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