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Area of a circle

Area of a circle

Area of a circle

A circle is one of the most simple objects. It is a shape that has a round shape and can be drawn in curves and lines. A circle is described by having two points with a radius. The area of a circle is calculated by making the area of a circle equal to the product of the radii multiplied by the square of the radius.The area of a circle formula is useful for measuring the region occupied by a circular field or a plot. Suppose, if you have a circular table, then the area formula will help us to know how much cloth is needed to cover it completely. The area formula will also help us to know the boundary length i.e., the circumference of the circle. Does a circle have volume? No, a circle doesn't have a volume. A circle is a two-dimensional shape, it does not have volume. A circle only has an area and perimeter/circumference. Let us learn in detail about the area of a circle, surface area, and its circumference with examples.

LENGHT

Circumference: The circumference of the circle is equal to the length of its boundary. This means that the perimeter of a circle is equal to its circumference. The length of the rope that wraps around the circle's boundary perfectly will be equal to its circumference. The below-given figure helps you visualize the same. The circumference can be measured by using the given formula:A circle can be divided into many small sectors which can then be rearranged accordingly to form a parallelogram. When the circle is divided into even smaller sectors, it gradually becomes the shape of a rectangle. We can clearly see that one of the sides of the rectangle will be the radius and the other will be half the length of the circumference, i.e, π. As we know that the area of a rectangle is its length multiplied by the breadth which is π multiplied to 'r'. Therefore, the area of the circle is πr to varying degrees of mathematical rigor. The most famous of these is Archimedes' method of exhaustion, one of the earliest uses of the mathematical concept of a limit, as well as the origin of Archimedes' axiom which remains part of the standard analytical treatment of the real number system. The original proof of Archimedes is not rigorous by modern standards, because it assumes that we can compare the length of arc of a circle to the length of a secant and a tangent line, and similar statements about the area, as geometrically evident

Following Satō Moshun (Smith & Mikami 1914, pp. 130–132) and Leonardo da Vinci (Beckmann 1976, p. 19), we can use inscribed regular polygons in a different way. Suppose we inscribe a hexagon. Cut the hexagon into six triangles by splitting it from the center. Two opposite triangles both touch two common diameters; slide them along one so the radial edges are adjacent. They now form a parallelogram, with the hexagon sides making two opposite edges, one of which is the base, s. Two radial edges form slanted sides, and the height, h is equal to its apothem (as in the Archimedes proof). In fact, we can also assemble all the triangles into one big parallelogram by putting successive pairs next to each other. The same is true if we increase it to eight sides and so on. For a polygon with 2n sides, the parallelogram will have a base of length ns, and a height h. As the number of sides increases, the length of the parallelogram base approaches half the circle circumference, and its height approaches the circle radius. In the limit, the parallelogram becomes a rectangle with width πr and height r. (Source: en.wikipedia.org)

 

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