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.