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Geometry 10-7 Area and Circumference of a Circle

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Geometry 10-7 Area and Circumference of a Circle Powered By Docstoc
					Presented by MJ Lund
   If a circle has a circumference of C units and a
    radius of r units, then C = 2πr.
   If a circle has an area of A square units and a
    radius of r units, then A = πr2




                                              r
Example #1:
Find the area of the shaded region
                                              18 yd
Solution:

Plan: Area of square - Area of the circle

Formulas: A = s2 –      πr2

            A = 502 - π182

            A = 2500 - 324π sq yds
                                            50 yd
        or A = 1482.12 sq yds.
                                      y


                                                     x
  Example #2:
                                          (2,-5)
                                  9
  Find the area of a circle
  with the equation
  (x-2)2 + (y+5)2 = 81



•This is a circle whose center point is (2,-5) and
  whose radius is 9.
•Therefore, A = π r2 and A = (π)(9)2 and so the
  A = 81π or about 254.5 sq units
Area of a Sector
   What is a “sector”?

  A sector is a section of the circle bound by two radii and their
                          intercepted arc.


    In simpler terms, the shape of a slice of pizza.



                             sector
Calculating the area of a sector

     Once again, you are confronted with
      another formula. Here is the area
      of a sector formula:
                                     mAB
                      Area    r   2

                                     360
   The formula calculates the total area of the circle first, then the
   formula takes the arc measure and divides by 360 to calculate
             the portion of the total area called a sector.
Area of a sector example #3:
 Given the following information with the
  diagram, calculate the area of the sector.

                                             mAB
                          Area    r 2 
                                             360
                                             120
                          Area    5 
                                         2         Plug in numbers for variables
                                             360
                                             1
A
      5 cm                Area    25             Simplified values
                                             3
             120
                                   25
                          Area                      Multiplied
                                    3
                                   78.54           2
                          Area           26.18cm       Final answer
                                     3
                    B
Calculating the area of a
        segment
What’s a segment?
A segment of a circle is a region bounded by a chord and its
                       intercepted arc.
Segment calculation process

  1. Calculate the area of the sector.
  2. Calculate the area of the triangle in
  the sector.
  3. Subtract the area of the triangle
  from the area of the sector.
Segment example #4:
Given the following information with the diagram,
 calculate the area of the segment of the circle.

                                         mAB
                        sector    r 
                                      2
                                                     Area of sector formula
        A                                360

                                              90
                        sector   12 
                                          2         Plug in values for variables
                                              360
                                              1
                        sector   144              Simplified
                    B                         4
       O
                                   144
            12 yd

                        sector                        Multiplied
                                     4
                        sector  36 113.1yd 2           Sector answer




                                                            continue
Segment example #4 continued:
Now that you have calculated the sector, calculate
 the area of the triangle inside the sector.

                                    1
        A            triangle        b  h          Area of a triangle formula
                                    2
                                   1        The base and height are 12 because each
                         triangle  12 12       represent radii of the circle.
                                   2
                                       1           Multiplied
                          triangle      144
                     B                 2
       O
                         triangle  72yd 2
             12 yd                                 Multiplied




                                                                 continue
Segment example #4 concluded:
 The last stage is to subtract the area of the
  triangle from the area of the sector.

                          segment  sector  triangle
         A

                          segment  113.1yd 2  72yd 2       Plug in values



                             segment  41.1yd 2         Final answer

                      B
        O     12 yd




                      Segment area = 41.10 square yds

				
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