Why area of the circle is πr2? | English

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Have you ever wondered why area of the circle is πr^2? Is there a way to visually prove that formula? In this video, we’ll convert the circle into a rectangle and understand how area of circle can be calculated using this trick.

Dear Friends,
Mathematics is fun when you understand the real meaning of the concept and apply it in various situations. It is often difficult to remember the formula and reproduce it whenever required.
In this video we will be discussing why the area of circle is πr^2 by experimental method. You can yourself derive the formula instead of just memorizing it and understand the real meaning of it.

Let us begin,
PROCEDURE
Area of the circle is the space occupied by the circle, so take a cutout of the circle.
Fold it in exact half to form a semicircle and then one more fold to make a quarter.
You can have one more fold across the radius to make 8 equal parts of the circle.
Now draw the lines with a marker and cut the lines to get 8 triangular figures (sectors of the circle)
Arrange them into a rectangular shape as shown in the figure. The last one can be cut exactly at the center to get a rectangular figure.
You can observe that this rectangle has curved surfaces at its length. Now what should be done?
Divide the circle into 16 equal parts and arrange to form a rectangle.
You may observe that the curves surface has been minimized. Similarly, you can go on making more parts of the circle to get almost rectangular figure.
The circle has been converted into the rectangle, thus the area of the circle would be same as the area of the rectangle.
We have,
Area of the circle = Area of the rectangle
We know that area of rectangle = l X b
Here, the circumference of the circle is converted into 2 lengths and the breadth of the rectangle is same as the radius of the circle.
Thus,
l x b = 1/2(2 πr ) X r
= πr^2
Hence,
Area of the circle = πr^2
In this way, you have derived the formula and now you know the reason why area of the circle is πr^2 ?
Hope you had fun visualizing the formula πr^2 and learned something new.

Team: Ashok Rupner, Chaitanya Mungi, Shanti Pise, Neha Apte
Music: Dr. Manasi Kulkarni