Area of Circular Sector
The area of a circular sector is the measure of the region enclosed by the two radii and the arc of the sector. It is calculated using the formula A = (θ/360)πr², where θ is the central angle of the sector and r is the radius of the circle. This concept is important in geometry and trigonometry for calculating areas of sectors in circles.
4 Key excerpts on "Area of Circular Sector"
eBook - ePub- Surinder Virdi, Roy Baker, Narinder Kaur Virdi(Authors)
- 2014(Publication Date)
- Routledge(Publisher)
...CHAPTER 11 Areas (1) Learning outcomes: (a) Calculate the areas of triangles, quadrilaterals and circles (b) Identify and use the correct units (c) Solve practical problems involving area calculation 11.11 Introduction Area is defined as the amount of space taken up by a two-dimensional figure. The geometrical properties of triangles, quadrilaterals and circles have been explained in Chapter 10. A summary of the formulae used in calculating the areas and other properties of these geometrical shapes is given in Table 11.1. The units of area used in metric systems are: mm 2, cm 2, m 2 and km 2. Table 11.1 Shape Area and other properties Area = l × b Perimeter = 2 l + 2 b = 2(l + b) Area = l × l = l 2 Perimeter = 4 l Area = l × h Area = π r 2 Circumference = 2π r 11.2 Area of triangles There are many techniques and formulae that can be used to calculate the area of triangles. In this section we consider the triangles with known measurements of the base and the perpendicular height, or where the height can be calculated easily. Example 11.1 Find the area of the triangles shown in Figure 11.1. Figure 11.1 Solution: (a) Base BC = 8 cm We need to calculate height AD, which has not been given. As sides AB and AC are equal, BD must be equal to DC. Therefore, BD = DC = 4 cm. Now we can use Pythagoras’ Theorem to calculate height AD : Therefore (b) 11.3 Area of quadrilaterals A plane figure bounded by four straight lines is called a quadrilateral. The calculation of area of some of the quadrilaterals is explained in this section. Example 11.2 Find the area of the shapes shown in Figure 11.2. Figure 11.2 Solution: (a) Area of a rectangle = length × width Length = 15 cm, and width = 6 cm Area of rectangle ABCD = 15 × 6 = 90 cm 2 (b) In a square, the length is equal to the width...
- Rebecca Dayton(Author)
- 2013(Publication Date)
- Research & Education Association(Publisher)
...Chapter 9 Circles Your Goals for Chapter 9 1. You should be able to identify the parts of a circle. 2. You should be able to determine the measure of arcs and the angles created in a circle. 3. You should be able to solve problems using circumference, arc length, and areas of circles and sectors. 4. You should be able identify the center and radius of a circle and graph the circle on a coordinate plane from an equation in center-radius form. 5. You should be able to write an equation of a circle given the center and radius. Standards The following standards are assessed on Florida’s Geometry End-of-Course exam either directly or indirectly: MA.912.G.6.2: (Low) Define and identify: circumference, radius, diameter, arc, arc length, chord, secant, tangent and concentric circles. MA.912.G.6.4: (Moderate) Determine and use measures of arcs and related angles (central, inscribed, and intersections of chords, secants and tangents). MA.912.G.6.5: (High) Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors. MA.912.G.6.6: (Moderate) Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius form, state the center and the radius of the circle. MA.912.G.6.7: (Moderate) Given the equation of a circle in center-radius form or given the center and the radius of a circle, sketch the graph of the circle. Lines and Segments A radius is a segment whose endpoints are the center and any point on the circle. A chord is a segment whose endpoints are on the circle. A diameter is a segment whose endpoints are on the circle and passes through the center. A diameter is the longest chord of the circle. A secant is a line that intersects the circle at two points. A tangent is a line that intersects the circle at exactly one point. Example: Identify each of the following in the given circle. A. chord B. secant C...
eBook - ePubDyslexia, Dyscalculia and Mathematics
A practical guide
- Anne Henderson(Author)
- 2013(Publication Date)
- Routledge(Publisher)
...the: radius — r, diameter — D, circumference — C. Figure 9.16 Properties of a circle Circle facts ● The circumference is the perimeter of a circle. ● The diameter is twice the length of the radius. ● The radius is half the length of the diameter (divide D by 2). ● Pi π (pronounced pie) is important. ● Pi π has a value of 3.142. ● Press EXP on the calculator to use π. ● A 3D shape with circular top and bottom is a cylinder. To find the circumference of a circle: (answer is in units) π × D or π × 2r A rhyme to help: Fiddle de-dum, Fiddle de-dee The ring round the moon is π times D. Figure 9.17 How to find the circumference of a circle To find the area of a circle (answer is in units 2) π × radius × radius which is written πr 2 A rhyme to help: A round hole in my sock Has just been repaired. The area mended Is pi r squared. Figure 9.18 How to find the area (A) of a circle Polygons ● Copy, cut out, stick onto card and turn the angle pictures and facts given into a memory card. (number 23, see page 144). ● Multi-sided figures are generally called polygons. They have individual names depending on the number of sides, but many students find these difficult to remember. Figure 9.19 Polygons Section E: Co-ordinates The two straight lines at right angles to each other on a graph are called the axes. Coordinates are a pair of numbers, usually in brackets, which describe the precise location of a point on the axes. The one which is horizontal is called the x -axis (because x is a cross) and the vertical line is called the y -axis. The first number indicates the x -axis value (across the hall) and the second number indicates the y -axis value (up the stairs). For example: (3, 5) means 3 units across to the right and 5 units up. Figure 9.20 Graph to show the position of co-ordinate (3,5) Section F: Rotational symmetry This is the description given when a pattern is rotated around a point to identify the number of times the pattern is repeated...
- Alfred Posamentier, Stephen Krulik(Authors)
- 2016(Publication Date)
- Routledge(Publisher)
...Using a toy dart set is preferred for classroom use rather than the archery set! Topic: Developing the Formula for the Area of a Circle Materials or Equipment Needed Construction paper prepared as shown in figures 9.1 and 9.2. Implementation of the Motivation Strategy Students are often “told” that the area of a circle is found by the formula A = π r 2. Too often, they are not given an opportunity to discover where this formula may have come from or how it relates to other concepts they have learned. It is not only entertaining, but also instructionally sound, to have the formula evolve from previously learned concepts. Assuming that the students are aware of the formula for finding the area of a parallelogram, this motivator presents a nice justification for the formula for the area of a circle. This motivational activity will use the teacher-prepared materials—a convenient size circle drawn on the piece of cardboard or construction paper, divided into 16 equal sectors (see figure 9.1). This may be done by marking off consecutive arcs of 22.5° or by consecutively dividing the circle into two parts, then four parts, then bisecting each of these quarter arcs, and so on. These sectors, shown in figure 9.1, are then to be cut apart and reassembled in the manner shown in figure 9.2. Figure 9.1 Figure 9.2 This placement suggests that we have a figure that approximates a parallelogram. That is, were the circle cut into more sectors, then the figure would approach a true parallelogram. Let us assume it is a parallelogram. In this case the base would have length, where C = 2π r (r is the radius). The area of the parallelogram is equal to the product of its base and altitude (which here is r). Therefore, the area of the, which is the commonly known formula for the area of a circle. This should certainly impress your students to the point where this area formula begins to have some intuitive meaning...
