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MENSURATION. 201
TABLE No. 23.—Areas of Segments of a Circle.
The diameter of a circle = 1, and it is divided into 100
equal parts.
h
Area. ±_ Area.
h
Area.
D D D
0.01 0.001329 0.18 0.096135 0.35 0.244980
0.02 0.003749 0.19 0.103900 0.36 0.254551
0.03 0.006866 0.20 0.111824 0.37 0.264179
0.04 0.010538 0.21 0.119898 0.38 0.273861
0.05 0.014681 0.22 0.128114 0.39 0.283593
0.06 0.019239 0.23 0.136465 0.40 0.293370
0.07 0.024168 0.24 0.144945 0.41 0.303187
0.08 0.029435 0.25 0.153546 0.42 0.313042
0.09 0.035012 0.26 0.162263 0.43 0.322928
0.10 0.040875 0.27 0.171090 0.44 0.332843
0.11 0.047006 0.28 0.180020 0.45 0.342783
0.12 0.053385 0.29 0.189048 0.46 0.352742
0.13 ’
0.059999 0.30 0.198168 0.47 0.362717
0.14 0.066833 0.31 0.207376 0.48 0.372704
0.15 0.073875 0.32 0.216666 0.49 0.382700
0.16 0.081112 0.33 0.226034 0.50 0.392699
0.17 0.088536 0.34 0.235473
Table No. 23 gives the areas of segments from 0.01 to 0.5
in height when the diameter of the circle is 1.
The area of any segment is computed by the following
rule:
Divide the height of the segment by the diameter of its
corresponding circle. Find in the table in column marked
—p the number which is nearest, and multiply the corresponding
area by the square of the diameter of the circle, and the
product is the area of the segment.
Example.
Figure the area of a segment of a circle, the height of the
segment being 12 inches and the diameter of the circle 40 inches.
Solution
:
12 divided by 40 = 0.3
In the column marked —p find 0.3; the corresponding
area is 0.198168.
The area of the segment is 40 X 40 X 0.198168 = 317.0688
square inches, or 317 square inches.
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