# Concentric Circle Problem

Someone at work showed me this today. I like it!

## 17 thoughts on “Concentric Circle Problem”

1. bellringer187868 says:

25 pi cm

• B.MURRAY says:

The area is surely in cm^2.

2. Since the radius of the inner circle is arbitrary, make it zero, so the 10cm measurement is the orange circle’s diameter.

• Planx Constant says:

Wouldn’t that make it half of a 10cm diameter circle’s area, which is to say 25/2 pi cm^2?

In the other answers, it’s stated as 25pi, am I missing something?

• planxconstant says:

That would make it half the area of a 10cm diameter circle, which would be 25/2 pi cm^2, but you state the answer as 25 pi. Am I missing something?

• planxconstant says:

Nevermind, I WAS missing something.

3. Spike says:

4. Arkarup Banerjee says:

25*pi

By varying the arbitrary inner radius an equally varied range of areas can be encompassed by the shaded area.
A simple exercise with pencil and compass confirms this.
If the ends of the 10cm line are A & B , its mid point is D and the centre of the circles is C ;
a generalised formula for the shaded area might read : ( pi times the square of the inner radius CD times the angle ACD over 360) minus 5CD square cm.