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Area and Volume

VIEWS: 4 PAGES: 11

									    Geometric
   Measurements
Fundamental Tools for Mathematical
            Modeling
Geometric Measurements

        Area
Geometric Measurements
        Area:
    The measurement of
 planar or curved surfaces
 expressed in square units.
                     AREA
   Calculate the Playing Area of a Football Field
                 From goal line to goal line


            300’                               Area  S1  S 2
                                               Area  300'150'
            S1
                                               Area  4500 ft    2



                        S2          150’



Note: 1 acre = 43,560 square foot
     The Area of a Circle
    Note: This is a small circle with a radius equal to that
     of the corner radius of the GEARS-IDS 6x9 Plate.
Radius = 0.250”
         a                Area(Circle)    R         2



                          Area(Circle)  3.14  0.025              2



                          Area(circle)  3.14  0.0625
                          Area(circle)  0.0122in              2


            D
                                                    = 3.14

 Diameter = 2R = 0.500”
     Calculating the Area of a Triangle
    Note: Segment ba is congruent to segment bc and
    segment da is congruent to segment dc. That information
    is given in the figure.
                                               1
                              Area(a, b, c)   base  height
                                               2
                  b                            1
                              Area(a, b, c)   6"4"
                                               2
4.0” S3               S2      Area(a, b, c)  12in2


              d
a                              c
                      3.0
              6.0”     ”
              S1
     Calculate the Area of the 6” x 9” Plate
                                           Corner Radius =0.250”

                                                      
                   8.688”
                                                          = 3.14
 Hole
 Dia.
 0.190”

                                                5.688”



 Note: A precise solution to this problem requires breaking the
               area up into multiple small areas

Don’t forget to subtract the area of all the holes!
The Surface Area of a Cylinder
  Parts of a Cylinder = 2 Circles + 1 Rectangle

  r
        SAcyl  2r  2rh      2


        Area of a Circle x 2
                               Area of a Rectangle with
                               Circumference as length


        h
            Length = Circumference
        Calculate the Surface Area of a
              Gear Head Motor
              3.850”
                           1.367”


                                    2.00” Dia.

1.55”




 SAcyl  2r  2rh    2
    Perimeter and Area of Basic Shapes
     s                                       P = 2l+2w or
         Perimeter = 4s or           l
s                      s+s+s+s                     2(l+w) or
                                 w
         Area =   s2                               l+w+l+w
                                                     A = lw


             P = s1 + s2 + s3
                                         C = 2r = d
         s                           r
    h        A = ½ bh
                                         A = r2
     b


    Quick Reference Slide
Go Forth and Calculate,
        The End
         For Now

								
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