Lab Manual: Area of Circle by Paper Cutting & Pasting Method | Lab Manuals for Class 10 PDF Download

Objective

• 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 = 1/2 x circumference of circle = 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.

Activity Time
Find out the area of a circle of radius 6.3 cm by dividing the circle into 32 sectors.