Give an activity to obtain the formula of area of a circle
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Answers
Answer:
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.
NCERT Class 10 Maths Lab Manual - Area of Circle by Paper Cutting and Pasting Method 1
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)
NCERT Class 10 Maths Lab Manual - Area of Circle by Paper Cutting and Pasting Method 2
Area of rectangle: length x breadth.
Sectors of a circle.
NCERT Class 10 Maths Lab Manual - Area of Circle by Paper Cutting and Pasting Method 3
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
NCERT Class 10 Maths Lab Manual - Area of Circle by Paper Cutting and Pasting Method 4
Fold it once along the diameter to obtain two semicircles as shown in fig. (ii).
NCERT Class 10 Maths Lab Manual - Area of Circle by Paper Cutting and Pasting Method 5
Again fold the semicircle to get quarters of circle.
NCERT Class 10 Maths Lab Manual - Area of Circle by Paper Cutting and Pasting Method 6
Repeat this process of folding upto four folds and then it looks like a small sector as shown in fig. (iv).
NCERT Class 10 Maths Lab Manual - Area of Circle by Paper Cutting and Pasting Method 7
Press and unfold the circle. It is divided into 16 equal sectors.
NCERT Class 10 Maths Lab Manual - Area of Circle by Paper Cutting and Pasting Method 8
Colour half of this circle i.e. 8 parts with one sectors with colour say blue and remaining 8 sectors different colour say orange.
NCERT Class 10 Maths Lab Manual - Area of Circle by Paper Cutting and Pasting Method 9
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).
NCERT Class 10 Maths Lab Manual - Area of Circle by Paper Cutting and Pasting Method 10
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).
NCERT Class 10 Maths Lab Manual - Area of Circle by Paper Cutting and Pasting Method 11
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.
Learning Outcome
The figure formed by arranging 17 sectors of a circle is almost a rectangle.
As we increase the number of sectors of the circle, the figure of rectangle becomes better and better.
Through this activity, students will learn to find the approximate result for the area of a circle.
Step-by-step explanation:
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