Posted on: June 11, 2020 Posted by: Susan Johnsey Comments: 0
area of a sector
If you are asked to find the area of a sector (slice of circular pizza) then you have 3 things to do:  
1.  The sector is a portion of the circle. Find the fraction that represents that.   The full arc of the circle is 360 degrees. The arc in the diagram is 60 degrees. Thus the arc and the blue sector represent 60 of 360. Please reduce this fraction 60/360 to 1/6.
2.  Find the area of the circle. That means we need the radius.   Look at the diagram and you see that is 5 cm.  Thus the circle area =(pi)r2 = pi times 5 times 5 = 25pi (cm sq).
3.  Now we can find the area of the blue sector. The area of the blue sector is 1-sixth of the full circle. 1-sixth of 25pi  is 25pi/6.   Hope you recall fraction multiplication.   Area of the blue sector is 25pi divided by 6  or 25pi/6 (cm sq).

You can view an animation of this HERE. Try different arc or central angle measures and with the radius = 4.

Who ate the most pizza? Roberto purchased a 10-inch deluxe pizza which was cut into 5 congruent (equal) slices. His pizza is a circle and the cuts went through the center of the pizza. Roberto ate 4 of the 5 slices. Dean purchased an 8-inch by 12-inch deluxe pizza and the cuts created 6 congruent square slices. Dean ate 4 slices of his pizza. Let me know your answer with explanation or work, of course. No guessing. You can email me or use the contact page.

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