maths lab activity observation of a circle
Answers
Answer:
Step-by-step explanation:
Definition of circle: A circle is the locus of a point in a plane which moves in such a way that its distance from a fixed point remains constant. Fixed point is known as centre and the fixed distance is known as radius of the circle.
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Area of the circle: It is the measure of the region of the plane enclosed by it.
Circumference of the circle: Total length of its boundary.
(C = 2πr, where ris radius of the circle)
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Area of rectangle: length x breadth.
Sectors of a circle.
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Materials Required
White paper, coloured sketch pen, a pair of scissors, fevicol, geometry box.
Procedure
Draw a circle of any radius on a sheet of paper (Take r = 6.5 cm) using compass
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Fold it once along the diameter to obtain two semicircles as shown in fig. (ii).
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Again fold the semicircle to get quarters of circle.
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Repeat this process of folding upto four folds and then it looks like a small sector as shown in fig. (iv).
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Press and unfold the circle. It is divided into 16 equal sectors.
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Colour half of this circle i.e. 8 parts with one sectors with colour say blue and remaining 8 sectors different colour say orange.
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Cut these sixteen different sectors of circle.
Cut one of the sector of orange colour into two equal parts as shown in the fig. (vii).
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Arrange these seventeen sectors (one orange sector is divided in two parts) in alternate manner so that they form a rectangular shape as shown in fig. (viii).
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Observation
Area of the rectangular shape so formed with seventeen sectors is same as the area of circle.
Length of the rectangular shape = [latex]\frac { 1 }{ 2 }[/latex] x circumference of circle = [latex]\frac { 1 }{ 2 }[/latex] x 2πr = πr.
Breadth of the rectangular shape = radius of circle
∴ Area of the rectangle = L x B = πr x r = πr2 sq. units.
Result
Area of a circle with radius r = πr2.