Machinery's Handbook Pocket Companion

Mathematical Formulas and Tables

GEOMETRICAL FORMULAS

Areas and Dimensions of Plane Figures

Circle:


Lenght of arc for center angle of 1 = 0.008727 d

Lenght of arc for center angle of n = 0.008727 nd

Example: Find the area A and circumference C of a circle with a diameter of 2 inches.


Example: The area of a circle is 16.8 square inches. Find its diameter.


Circular Sector:


Example: The radius of a circle is 35 millimeters, and angle ? of a sector of the circle is 60 degrees. Find the area of the sector and the length of arc l.


Circular Segment:


Example: The radius r is 60 inches and the height h is 8 inches. Find the length of the chord c.


Example: If c = 16, and h = 6 inches, what is the radius of the circle of which the segment is a part?


Circular Ring:


Example: Let the outside diameter D = 12 centimeters and the inside diameter d = 8 centimeters Find the area of the ring.


By the alternative formula:


Circular Ring Sector:


Example: Find the area, if the outside radius R = 5 inches, the inside radius r = 2 inches, and ? = 72 degrees.


Spandrel or Fillet:


Example: Find the area of a spandrel, the radius of which is 0.7 inch.


Example: If chord c were given as 2.2 inches,...

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