Maths Project No: 2
Cutting a circle into equal section of small central angles to find the area of the circle by using the formula a=pie r2
Pre requesting knowledge
i. formula of the circumference of circle
ii. formula of area of rectangle
MATERIALS USED
1. Drawing sheet or white paper
2. Geometric Box
3. Colour Pencils
4. Scissors
5. Fevicol
Procedure
Procedure 1
Draw a circle of 6 cm radius on the drawing sheet.
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Procedure 2
Draw the diameter of the circle.
Procedure 3
Paint the halves of the circle in different colours.
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Procedure 4
Divide the circle into 8 equal halves by folding the paper for that first fold the circle to get 2 equal semicircle and continue folding till we have folded the circle 4 times and we will get a circle divided in 8 equal parts.
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Procedure 5
Now cut all these eight parts as shown in the figure 2.
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Procedure 6
Take any one part and cut in into 2 equal halves.
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Procedure 7
Paste all the parts of the circle on white sheet of paper exactly as shown in figure 3.
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OBSERVATION
In the figure 4 formed by pasting all seven parts and two halves of figure 3 at the ends, we observe that a rectangle is formed. We know that circumference of a circle with radius are are equal to 2лr and area of the rectangle = lxb. Here, length of the rectangle = ½x2лr which is лr and breadth of rectangle=radius of the circle = 2
Calculation = Area of the circle
= Area of the rectangle in figure 4
=lxb
=лr x r
=лr x r2
Result
Area of the circle of radius r units = лr2
Learning outcomes
1) Students learn the elinmentary concept of Changing another. I Geometrical shape into another .
2) Students learn the elementary concept of approximation by transforming a circle cente a shape like rectangle.
3) If the circle is further divided unto 16, 32, 64 equal parts. Then the figure 4 appears more and more like a rectangle and thus approximation keeps on getting better further.
4) Area of a circle is the geometrical intuition of the students.
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