Target Areas

By:

Allison Kootsikas


In the concentric circles below which has the greater area - the yellow region or the blue region?


My hypothesis is that both sections have the same area.  By eyeballing it, one might think the blue has more area, but I think that because the yellow is one the outside, it has more area to cover then the green and the same as the blue.


 

The first thing that I want to do is to find the area of the inner 3 rings of the circle. 

 

The formula for the area of a circle is A=πr2. 

p=3.14

r=radius (center of circle to outside edge.) 

 

I know that it is 1” between each ring of the circle.  Therefore, the radius of the entire blue circle is 3”.

 

A=π(32)

A=π(9)

A=28.27”

 

Next, I find the area for the green circle.  This will include the inner three rings.

 

A=π(42)

A=π(16)

A=50.27”

 

Next, find the area of the entire circle.

A=π(52)

A=π(25)

A=78.54”

 

To find the area of the yellow ring alone, I subtract the total area from the area of the inner 4 rings.

 

78.54”-50.27”=28.27”


The yellow area and the blue areas have the same area.