Question

cutting the circle into equal sections of a small central angle to find the area of a circle by using the formula A=π®2. please answer with full solutions please ​

Answer 1

Answer:

Cut a full circle into 2 semi circles first. Then divide each semicircle into 2 halves. Each half will be one quarter of full circle.

Then again cut each quarter circle int 2 halves….. This way go on cutting the circle into as many sectors as there are possible. As you increase the number of sectors , sector angle of each sector goes on decreasing…

Now, suppose we get 20 pieces of sectors. Arrange them one next to the other, in such a way that arc of one sector lies next to the central angle of the 2nd. Then arc of 3rd & then central angle of the fourth… & so on..

After arranging all 20, This arrangement looks like somewhat very close to a rectangle. we find that 10 arcs of 10 sectors are on one side. And 10 arcs of 10 sectors on the other side. These arcs can be considered as length of the rectangle & radius segment of the sector replaces the width of the rectangle.

Area of so obtained rectangle = area of circle (as circle is cut & converted into a rectangle)

Here length = pi r ( half of a circle is = length)

Width = r

So, area of rectangle = pi r * r = pi r²