Measurement
Table of Contents
- Circles
- Area of a Circle - Wedge/Sector Demonstration
- Area of Circles
- Rich Tasks
- '...in a square'
Area of a Circle - Wedge/Sector Demonstration
We know that the area of a circle is: A=πr². But this is actually hard to prove.[br][br]So we cut the circle into wedges and place half of the wedges face-up and half face-down. [br]The hanging-out yellow pieces always "fill-up" the empty areas of the rectangle with A=πr²[br][br]As the number of wedges increases, the teal line -> radius and the hanging-out pieces start to fit inside the rectangle.[br]Isn't that cool? Showing this mathematically is called calculus!
What is the total length of the curved parts of the yellow wedges?[br]Why did we label the x-axis with units of π and the y-axis with units of numbers?
'...in a square'
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A blue square is inscribed in a green square. Answer the questions below! |
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What fraction of the area of the green square is occupied by the blue square? What fraction of the perimeter of the the green square is the perimeter of the blue square? A blue rectangle is inscribed in a green square. What fraction of the area of the green square is occupied by the blue rectangle? What fraction of the perimeter of the the green square is the perimeter of the blue rectangle? |