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.
- Sectors of a circle.
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
- Fold it once along the diameter to obtain two semicircles as shown in fig. (ii).
- Again fold the semicircle to get quarters of circle.
- Repeat this process of folding upto four folds and then it looks like a small sector as shown in fig. (iv).
- Press and unfold the circle. It is divided into 16 equal sectors.
- Colour half of this circle i.e. 8 parts with one sectors with colour say blue and remaining 8 sectors different colour say orange.
- 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).
- 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 =
x circumference of circle =
- 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.
No comments:
Post a Comment