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Answers
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Activity 1
Area of Circle by Paper Cutting and Pasting Method
Objective
To obtain the formula for area of the circle i.e., πr2 by paper cutting and pasting method.
Prerequisite Knowledge
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.
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)
Area of rectangle: length x breadth.
Sector: When two radii meet at the center of a circle to form a sector
Materials Required
White paper, coloured sketch pen, a pair of scissors, fevicol, geometry box.
Procedure
1) Draw a circle of any radius on a sheet of paper (Take r = 6.5 cm) using compass
2) Fold it once along the diameter to obtain two semicircles as shown in fig. (ii).
3) Again fold the semicircle to get quarters of circle.
4) Repeat this process of folding upto four folds and then it looks like a small sector as shown in fig. (iv).
5) Press and unfold the circle. It is divided into 16 equal sectors.
6) Colour half of this circle i.e. 8 parts with one sectors with colour say blue and remaining 8 sectors different colour say orange.
7) Cut these sixteen different sectors of circle.
8) Cut one of the sector of orange colour into two equal parts as shown in the fig. (vii).
9) 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).
Observation
Area of the rectangular shape so formed with seventeen sectors is same as the area of circle.
Length of the rectangular shape = \frac { 1 }{ 2 } x circumference of circle = \frac { 1 }{ 2 } 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.
Answer:
pepar cuting and pasting dwra sarvsamika (a-b)2=a2+2ab+b2