1 / 13

How to find the area of a circle from segments

How to find the area of a circle from segments. Anuradha Datta Murphy University of Illinois at Urbana-Champaign. Outline of presentation: Concept of area Area expressed as mathematical formulae Definition of a circle and its components Concept of p How to find the area of a circle

eliza
Download Presentation

How to find the area of a circle from segments

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. How to find the area of a circle from segments Anuradha Datta Murphy University of Illinois at Urbana-Champaign

  2. Outline of presentation: • Concept of area • Area expressed as mathematical formulae • Definition of a circle and its components • Concept of p • How to find the area of a circle • Show Wolfram Demonstrations tutorial • Explanation of how to find the area of a circle from its segments • Suggestion of further exercises in area calculations

  3. What is area? • Area is defined as the size of a two-dimensional surface, typically enclosed by a closed curve.

  4. Areas expressed by mathematical formulas: • Areas of figures can be calculated using mathematical formulas. The following 2-dimensional figures have simple formulas for calculating their area: Square: area = S2, Where S is the length of one side S Triangle: area = ½ bxh, where b is the length of the base and h is the height h b Parallelogram: area = bh, where b is the length of any side, and h is the distance between the lines of b h b

  5. What is a circle? • A circle is defined as a curved line surrounding a central point, every point on the line being equidistant from the center. • In the figure below, the curve is equidistant from the point o, the center of the circle. • The distance r is defined as the radius of the circle. • The section aob is called a segment of the circle. o b r a

  6. What is p? • The distance around a circle is called its circumference. • The distance across a circle through its radius (i.e., twice the radius) is called its diameter. • The Greek letter p is used to represent the ratio of the circumference of a circle to its diameter. d = 2r Circumference, c =pd p= c/d = 3.14 d .

  7. Area of a circle: • The area enclosed by a circle with radiusr is Area = pr2 Or,given a diameter d, Area = p(d/2)2 = (pd2)/4 r d

  8. Viewing Wolfram Demonstration on how to find area of a circle from segments: • Go to the Wolfram Demonstrations Project site at http://demonstrations.wolfram.com/ • Type “area” in the Search window • From the search results, select “Area of a Circle from Segments” by clicking on it • Click on “watch web preview” to view a short demonstration

  9. Viewing the Wolfram Demonstration: • In the demonstration, the circle is divided into many segments. These segments are stacked on the side of the circle. segments

  10. Viewing the Wolfram Demonstration (contd.): • As the number of segments increases, the stack resembles a rectangle. Since the circumference of the circle is 2pr, the rectangle has sides r and pr. Area of rectangle = pr x r = pr2 and, Area of circle =pr2 r pr Circumference = 2pr

  11. Viewing the Wolfram Demonstration (contd.): • To view the Wolfram Demonstration interactively, click on the “Download Live Version” button on the demonstration screen • *Note*: Mathematica Player has to be installed on your desktop before this application can be run • In the Live Version of the demonstration, you can change the number of segments in the circle by clicking on the slider. As you change the number of segments, observe that increasing the number makes the stack of segments resemble a rectangle, which helps to illustrate the formula for calculating the area of a circle.

  12. Further exercises in area calculation: • Return to the area search results page. • Select at least three other shapes and view the demonstrations on area calculations for each of these. For example, you could try the following: • Area of a Parallelogram • Area of a Triangle as Half a Rectangle • Maximizing the Surface Area of a Cylinder with a Fixed Volume

  13. Closing Notes: • For further illustrations on calculating the area of circles, take a look at: • http://www.easycalculation.com/area/learn-circle.php • http://www.wikihow.com/Calculate-the-Area-of-a-Circle • http://www.mathwarehouse.com/geometry/circle/area-of-circle.php • For more examples of simple area calculations, see: • http://en.wikibooks.org/wiki/Geometry/Area • http://www.webmath.com/index5.html • http://www.kidsnewsroom.org/elmer/infocentral/geometry/Area.html

More Related