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how to derive the formula of area of circle. This page looks to give a general run through of how the formula for the area of a circle can be derived. Here the Greek letter p represents the constant ratio of the circumference of any circle to its diameter approximately equal to 314159.
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We give the angle between the two radii as d. One method of deriving this formula which originated with Archimedes involves viewing the circle as the limit of a sequence of regular polygons. The area of the rectangles can then be calculated as.
The Area of Circle formula is.
Now to get the total area of the circle we have to integrate this elementry area using calculus. A 2p 0 R 0 rdrdth pR2 Let us evaluate the integral A 2p 0 R 0 rdrdth. 1 The same rectangle is present four times in the circle once in each quarter of it. The circumference unwraps to form a straight line and the circle opens up like the petals of a flower.
