A Pizza Problem

Here is your slice of pizza.


 
Can you tell from this slice how many pieces there were in the original pie and how big around is it? If you examine the typical pie (on the right), you will see that it is usually cut into 8 pieces. Measure the "angle width" of the marked slice. (It's the part of the slice that goes into your mouth first and burns your upper palatte.)

Use a circular protractor to measure this angle (ABC).  You should get 45 degrees.

What about the measure of all the other  angles touching the center? If you said they had to be the same, then you were right! Now if you count the angles (also known as central angles) you will find that there are 8 such angles. Each one is 45 degrees. So how many degrees are there in all 8 slice angles? 

(45 X 8 = 360 degrees ) 

Let's say that the slice you have has a slice angle of 30 degrees. How many slices did the original pie have? If the length of the crust arc is 3.5 inches, how round was your pie?

See figure for a hint.

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