How to create an Illustrator multi-color arc shapes, create a circle, hold down the shift key to make it a circle via the ellipse tool found in the tools panel of the application.
You will see a little control on the circle at the side and you can select that and drag that around to create a gap in the design, creating an arc form for the design / pie slice shape.
You can now add a color to this but you can also add multiple colors to the design by using the appearance panel and adding more fills via the right side and setting the colors for each of those. With each of these entries you will need to add an effect and distort and transform and the transform command and once in the dialog set the scaling to 90% and 90%. You can now duplicate that fill / transform entry and change the color. Double click the transform and set the scaling this time to 80% and 80% and then repeat that multiple times with different fills such as red, green, blue, purple etc
It is still live. Check out the video to see how you can create amazing multi-color arc designs in seconds using this technique.