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Segments of Circles:: The Arc, Chord, Radius, Height, Angle, Apothem, and Area

The document discusses different variables related to segments of circles such as arc length, chord length, radius, height, angle, apothem, and area. It provides values for these variables given two input variables in different cases. It also shows the numerical methods used to calculate some of the variables in different cases.

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Kevin McGrath
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75 views2 pages

Segments of Circles:: The Arc, Chord, Radius, Height, Angle, Apothem, and Area

The document discusses different variables related to segments of circles such as arc length, chord length, radius, height, angle, apothem, and area. It provides values for these variables given two input variables in different cases. It also shows the numerical methods used to calculate some of the variables in different cases.

Uploaded by

Kevin McGrath
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as XLS, PDF, TXT or read online on Scribd
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Segments of Circles:

The Arc, Chord, Radius, Height, Angle, Apothem, and Area

Enter any two of the variables to obtain the rest Given s, c s, r s, h


Case 1 Case 2 Case 3
Arc length 90 s 90 90 90
Chord Length c 0 #DIV/0! 88.92433
Radius r 14.32394 0 167.7404
Height (outside radius to chord midpoint) 6 h 28.64789 #DIV/0! 6
Angle (in radians) theta 6.283185 #DIV/0! 0.536544
Angle (in degrees) theta 360.0106 #DIV/0! 30.74259
Apothem (distance from chord to center circle) d -14.3239 #DIV/0! 161.7404
Area K 644.5775 #DIV/0! 356.9895

Given r, h r, theta r, d
Case 12 Case 13 Case 14
s #DIV/0! 0 #DIV/0!
c #DIV/0! 0 #DIV/0!
r 0 0 0
h 6 0 0
theta #DIV/0! 0 #DIV/0!
theta #DIV/0! 0 #DIV/0!
d -6 0 0
K #DIV/0! 0 #DIV/0!
Numerical Method for Case 1
case 1
k 0
n x(n) sin(x(n)) cos(x(n))sin(x(n))/x(n)
0 2.44949 0.638158 -0.76991 0.260527
1 3.278367 -0.13635 -0.99066 -0.04159
2 3.140733 0.000859 -1 0.000274
3 3.141593 -2E-010 -1 -7E-011
4 3.141593 1.2E-016 -1 3.9E-017
5 3.141593 1.2E-016 -1 3.9E-017
6 3.141593 1.2E-016 -1 3.9E-017
Numerical Method for Case 3, 5, 6, 11, 15, 18, 21
case 3 case 5 case 6 case 11
k 0.133333 0 0 #DIV/0!
n x(n) x(n) t(n) t(n)
0 0.266667 1.414214 0 #DIV/0!
1 0.268281 1.572089 #DIV/0! #DIV/0!
2 0.268272 1.570796 #DIV/0! #DIV/0!
3 0.268272 1.570796 #DIV/0! #DIV/0!
4 0.268272 1.570796 #DIV/0! #DIV/0!
5 0.268272 1.570796 #DIV/0! #DIV/0!
6 0.268272 1.570796 #DIV/0! #DIV/0!
s, theta s, d s, K c, r c, h c, theta c, d c, K
Case 4 Case 5 Case 6 Case 7 Case 8 Case 9 Case 10 Case 11
90 90 90 #DIV/0! 0 #DIV/0! #DIV/0! #DIV/0!
#DIV/0! 57.29578 #DIV/0! 0 0 0 0 0
#DIV/0! 28.64789 #DIV/0! 0 3 #DIV/0! 0 #DIV/0!
#DIV/0! 28.64789 #DIV/0! #DIV/0! 6 #DIV/0! 0 #DIV/0!
0 3.141593 #DIV/0! #DIV/0! 0 0 #DIV/0! #DIV/0!
0 180.0053 #DIV/0! #DIV/0! 0 0 #DIV/0! #DIV/0!
#DIV/0! 0 #DIV/0! #DIV/0! -3 #DIV/0! 0 #DIV/0!
#DIV/0! 1289.155 0 #DIV/0! 0 #DIV/0! #DIV/0! 0

r, K h, theta h, d h, K theta, d theta, K d, K


Case 15 Case 16 Case 17 Case 18 Case 19 Case 20 Case 21
#DIV/0! #DIV/0! 18.84956 #DIV/0! 0 #DIV/0! #DIV/0!
#DIV/0! #DIV/0! 12 #DIV/0! 0 #DIV/0! #DIV/0!
0 #DIV/0! 6 #DIV/0! 0 #DIV/0! #DIV/0!
#DIV/0! 6 6 6 0 #DIV/0! #DIV/0!
#DIV/0! 0 3.141593 #DIV/0! 0 0 #DIV/0!
#DIV/0! 0 180.0053 #DIV/0! 0 0 #DIV/0!
#DIV/0! #DIV/0! 0 #DIV/0! 0 #DIV/0! 0
0 #DIV/0! 56.54867 0 0 0 0

sin(x(n))/x(n)

case 15 case 18 case 21


#DIV/0! 0 #DIV/0!
t(n) t(n) t(n)
#DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0!

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