THE AREA OF A CIRCLE An introduction to approximating the area of a circle.

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Presentation transcript:

THE AREA OF A CIRCLE An introduction to approximating the area of a circle.

PLAN – Use areas we already know We know the area of squares. Approximate the area of a circle by finding the area of squares: One inside the circle. One outside the circle.

Dimensions of the Circle and Squares

What is the area… of this big square?

What is the area… of this big square? Area = 2r x 2r = 4r2

What is the area… of the circle? Circle Area < 4r2

What is the area… of the small square?

What is the area… of the small square? Think… What other shapes is the small square made of?

What is the area… of the small square? Area = 2 x Triangle Area = 2 x ½ x 2r x r = 2r2

Small Square Area < Circle Area < Big Square Area What is the area… of the circle? Small Square Area < Circle Area < Big Square Area 2r2 < Circle Area < 4r2