Class 07 Activity – Area of Circle

 Activity – Area of Circle

Objective: 

To verify the formula for area of a circle. Or to verify the following formula.

Area of a circle = 𝜋 x (radius)²

Materials Required: 

Thick sheets of paper, colour pencils, a pair of scissors, glue stick, geometry box, etc.

Procedure:

On a thick sheet of paper, draw a circle of any convenient 

radius. Colour one-half of the circle. Using a pair of scissors, 

cut it out.

2. Divide the circular cutout into eight equal parts. This can be done by drawing two pairs of perpendicular diameters. Using a pair of scissors, cut out the sectors along the radii.

3. Arrange the 8 sectors of the circle as shown below, which is roughly a parallelogram.

4. Repeat step 1. Now, divide the circular cut out into 16 equal parts. Using a pair of scissors, cut out the sectors along the radii.

5. Arrange the 16 sectors of the circle as shown below.

6. Repeat the procedure. As we go on increasing the number of sectors, the length of arcs go on decreasing. The more the sectors we have the nearer we reach a rectangle.

Observations:

 1.In figure , AB = CD = radius of the circle.

 Also the whole circle is divided into 8 sectors and oneach side there are  4 sectors. The length of the parallelogram is the length of 4 sectors, which is half of the circumference of the circle. 

2. Similarly, in figure, AB = CD =  radius of the circle  and the length of the parallelogram is equal to half of the circumference of the circle.

3. In figure, AB = CD = Breadth of the rectangle ABCD = radius of the circle and BC =  AD = length of the rectangle, which is half of the circumference of the circle. 

Area of the circle = area of the rectangle 

= length x breadth

= 1/2 x 2 𝜋 r x r , where r is the radius of the circle.

= 𝜋 r²

Conclusion: 

From the above activity, it is verified that 

area of a circle= 𝜋 x (radius)² 

Do Yourself: 

Draw a circle of radius 5 cm. Verify the formula for area of a circle by paper cutting and Pasting method.