How To: Derive the area of a circle

Derive the area of a circle

This video is about deriving the area of a circle of radius 'r' using polar co-ordinate. First, we draw a circle and its radius 'r'. Then draw another radius close to it, so that it forms a small triangle-like figure. To find the area of the complete circle, divide the circle into similar small triangles. The area of each triangle is given by half the product of its perpendicular and the base. We give the angle between the two radii as d?. We get the area of the small triangle by substituting d? and using trigonometry. By integral calculus, we know that ? varies from 0 to last. Thus, we get the area of the complete circle as integral of dA as ? varies from 0, p. Then, substituting the formula of area of triangle with dA, and simplifying the equation further, we get that area of circle = pr*r.

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