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Circle Sector and Segment
Sometimes you might need to determine the area under an arc, or the area of a sector. A sector is a part of a circle that is shaped like a piece of pizza or pie.
In order to find the area of this piece, you need to know the length of the circle's radius. In addition to the radius, you need to know either the degree of the central angle, or the length of the arc.
With these measurements finding the area of a sector is a simple matter of plugging the numbers into given formulas. To calculate the area of a sector, start by finding the central angle of the sector and dividing it by Next, take the radius, or length of one of the lines, square it, and multiply it by 3. Then, multiply the two numbers to get the area of the sector.
Article Edit. Learn why people trust wikiHow. This article was co-authored by our trained team of editors and researchers who validated it for accuracy and comprehensiveness. Together, they cited information from 6 references.The sector of a circle is a partition of that circle. A sector extends from the center, or origin, of the circle to its circumference and encompasses the area of any given angle that also originates from the center of the circle. A sector is best thought of as a piece of pie, and the bigger the angle of the sector, the bigger slice of pie.
Each side of the segment is a radius of the circle. You can find the radius of both the sector and the circle by using the sector's angle and area. Double the area of the segment. For the example, the sector's angle is 60 degrees.
Divide the area doubled by the number obtained in the previous step. For the example, 48 divided by 1. Find the square root of that number. For the example, the square root of The radius of this segment is 6. Chance E. Gartneer began writing professionally in working in conjunction with FEMA. He has the unofficial record for the most undergraduate hours at the University of Texas at Austin. When not working on his children's book masterpiece, he writes educational pieces focusing on early mathematics and ESL topics.
About the Author. Photo Credits. Copyright Leaf Group Ltd.The circular flow of income or circular flow is a model of the economy in which the major exchanges are represented as flows of moneygoods and servicesetc. The flows of money and goods exchanged in a closed circuit correspond in value, but run in the opposite direction. The circular flow analysis is the basis of national accounts and hence of macroeconomics.
The idea of the circular flow was already present in the work of Richard Cantillon. Richard Stone further developed the concept for the United Nations UN and the Organisation for Economic Co-operation and Development to the system, which is now used internationally.
The circular flow of income is a concept for better understanding of the economy as a whole and for example the National Income and Product Accounts NIPAs. In its most basic form it considers a simple economy consisting solely of businesses and individuals, and can be represented in a so-called "circular flow diagram.
These activities are represented by the green lines in the diagram. Alternatively, one can think of these transactions in terms of the monetary flows that occur. Businesses provide individuals with income in the form of compensation in exchange for their labor.
That income is spent on the goods and services businesses produce. These activities are represented by the blue lines in the diagram above. The circular flow also illustrates the equality between the income earned from production and the value of goods and services produced. Of course, the total economy is much more complicated than the illustration above. An economy involves interactions between not only individuals and businesses, but also Federal, state, and local governments and residents of the rest of the world.
Also not shown in this simple illustration of the economy are other aspects of economic activity such as investment in capital produced—or fixed—assets such as structures, equipment, research and development, and softwareflows of financial capital such as stocks, bonds, and bank depositsand the contributions of these flows to the accumulation of fixed assets. One of the earliest ideas on the circular flow was explained in the work of 18th century Irish-French economist Richard Cantillon who was influenced by prior economists, especially William Petty.
Cantillon distinguished at least five types of economic agents: property owners, farmers, entrepreneurs, labors and artisans, as expressed in the contemporary diagram of the Cantillon's Circular Flow Economy. The model Quesnay created consisted of three economic agents: The "Proprietary" class consisted of only landowners.
The "Productive" class consisted of all agricultural laborers.
The "Sterile" class is made up of artisans and merchants. In Marxian economics, economic reproduction refers to recurrent or cyclical processes  by which the initial conditions necessary for economic activity to occur are constantly re-created. Economic reproduction involves the physical production and distribution of goods and services, the trade the circulation via exchanges and transactions of goods and services, and the consumption of goods and services both productive or intermediate consumption and final consumption.
Karl Marx developed the original insights of Quesnay to model the circulation of capital, money, and commodities in the second volume of Das Kapital to show how the reproduction process that must occur in any type of society can take place in capitalist society by means of the circulation of capital. Marx distinguishes between "simple reproduction" and "expanded or enlarged reproduction". In the capitalist mode of production, the difference is that in the former case, the new surplus value created by wage-labour is spent by the employer on consumption or hoardedwhereas in the latter case, part of it is reinvested in production.
Keynes' assistant Richard Stone further developed the concept for the United Nations UN and the Organisation for Economic Co-operation and Development to the systems, which is now used internationally.
The first to visualize the modern circular flow of income model was Frank Knight in publication of The Economic Organization. Knight pictured a circulation of money and circulation of economic value between people individuals, families and business enterprises as a group,  explaining: "The general character of an enterprise system, reduced to its very simplest terms, can be illustrated by a diagram showing the exchange of productive power for consumption goods between individuals and business units, mediated by the circulation of money, and suggesting the familiar figure of the wheel of wealth.
A circular flow of income model is a simplified representation of an economy. In the basic two-sector circular flow of income model, the economy consists of two sectors : 1 households and 2 firms. In addition, the model assumes that a through their expenditures, households spend all of their income on goods and services or consumption and b through their expenditureshouseholds purchase all output produced by firms. The firms then spend this all of this income on factors of production such as labor, capital and raw materials, "transferring" all of their income to the factor owners which are households.
The factor owners householdsin turn, spend all of their income on goods, which leads to a circular flow of income.Find the length of its arc and area. Find the area of the shaded region. Find the length of the pendulum. Find the area swept by the minute hand in one minute. Clearly, minute hand of a clock describes a circle of radius equal to its length i. Find the area of the sector. Let OAB be the given sector. Find the area of the face of the clock described by the minute hand between 9 A.
Find the sum of distances travelled by their tips in 2 days. In 2 days, the short hand will complete 4 rounds. One point on the belt is pulled directly away from the centre O of the pulley until it is at P, 10 cm from O. Find the length of the belt that is in contact with the rim of the pulley.
Circles, Arcs and Sectors
Also, find the shaded area. Clearly, portion AB of the belt is not in contact with the rim of the pulley. Find the radius of the circle. Assuming umbrella to be a flat circle of radius 45 cm. Find the area between the two consecutive ribs of the umbrella. Since ribs are equally spaced.
The wire also used in making 5 diameters which divide the circle into 10 equal sectors as shown in Fig. Find: i the total length of the silver wire required ii the area of each sector of the brooch. Your email address will not be published. Comments Good information Right guidance. Leave a Reply Cancel reply Your email address will not be published.
We will now look at the formula for the area of a sector where the central angle is measured in degrees. Comparing the area of sector and area of circle, we derive the formula for the area of sector when the central angle is given in degrees. Worksheet to calculate arc length and area of a sector degrees. Given that the radius of the circle is 5 cm, calculate the area of the shaded sector.
We can calculate the central angle subtended by a sector, given the area of the sector and area of circle. The area of a sector with a radius of 6 cm is Calculate the angle of the sector. Next, we will look at the formula for the area of a sector where the central angle is measured in radians. Comparing the area of sector and area of circle, we get the formula for the area of sector when the central angle is given in radians.
Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations. We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page. Related Topics: More Geometry Lessons Geometry Games In these lessons, we will learn the area of a sector in a circle the formula for area of sector in degrees the formula for area of sector in radians how to calculate the central angle of a sector how to calculate the radius of a sector how to calculate the area of a segment.
The following table gives the formulas for the area of sector and area of segment for angles in degrees or radians. Scroll down the page for more explanations, examples and worksheets for the area of sectors and segments. Area of Sector A sector is like a "pizza slice" of the circle.
The following diagrams give the formulas for the area of circle and the area of sector. Scroll down the page for more examples and solutions. Formula for Area of Sector in degrees We will now look at the formula for the area of a sector where the central angle is measured in degrees. You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.A circular sector or circle sector is the portion of a disk enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector.
Reference: Wikipedia Circular Sector. This article is contributed by Chinmoy Lenka. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute. See your article appearing on the GeeksforGeeks main page and help other Geeks. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
Writing code in comment? Please use ide. SectorArea radius, angle. Python program to find Area of a Sector. Constraint or Limit.
Calculating area of the sector. WriteLine "Angle not possible". WriteLine sector. Recommended Posts: Program to find area of a Circular Segment Check whether a point exists in circle sector or not. Calculate Volume, Curved Surface Area and Total Surface Area Of Cylinder Find area of the larger circle when radius of the smaller circle and difference in the area is given Longest rod that can be inserted within a right circular cylinder Largest right circular cylinder within a cube Largest right circular cylinder within a frustum Largest cube that can be inscribed within a right circular cylinder Volume of largest right circular cylinder within a Sphere Volume of biggest sphere within a right circular cylinder Largest right circular cylinder that can be inscribed within a cone Largest right circular cone that can be inscribed within a sphere Largest cube that can be inscribed within a right circular cone Minimum number of Circular obstacles required to obstruct the path in a Grid Area of a Hexagon.
Load Comments.A circular sector is a wedge obtained by taking a portion of a disk with central angle radiansillustrated above as the shaded region. A sector with central angle of radians would correspond to a filled semicircle. Let be the radius of the circlethe chord length, the arc lengththe sagitta height of the arced portionand the apothem height of the triangular portion. The angle obeys the relationships. It follows that the weighted mean of the is. Gearhart and Schulz Checking shows that this obeys the proper limits for a semicircle and for an isosceles triangle.
Beyer, W. Gearhart, W. Harris, J. New York: Springer-Verlag, pp. Kern, W. Solid Mensuration with Proofs, 2nd ed. New York: Wiley, p. Weisstein, Eric W. Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more.