how to derive area of a circle

Asked by sahil.95rana | 23rd Feb, 2010, 08:00: PM

Expert Answer:

If we divide the area into equal parts we intially get a semicircle, and further dividing them, we'll get quadrants.

The quadrant can be still be divided into smaller parts uptil the arc is approximately equal to straight line distance and we get an isoceles triangles, we'll know how many such triangles would make up the circle.

Find the area of such a triangle, multiply by the total number of such triangles. and we can calculate the area of the circle by πR2.

Compare the two results and you'll find they match.

You can do it for circles with different Radii, and verify the equation.

The formula can be derived by methods of calculus, See Class XI OR XII mathematics book, if required.




Answered by  | 24th Feb, 2010, 07:21: AM

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