This section is from the book "Applied Science For Metal Workers", by William H. Dooley. Also available from Amazon: Applied Science For Metal Workers.
The forms of most tanks, compartments, and mechanical parts are those of simple geometrical figures such as squares, rectangles, hexagons, ellipses, and circles. Every pupil should be able to find the area and volume of such figures quickly and accurately. The following rules will be of assistance:
Rules Relative to the Circle
To Find Circumference:
Multiply diameter by 3.1416 Or divide diameter by .3183
To Find Diameter:
Multiply circumference by .3183 Or divide circumference by 3.1416
To Find Radius:
Multiply circumference by .15915 Or divide circumference by 6.28318
To Find Area:
Multiply circumference by one-quarter of the diameter
* For a more extended discussion of practical mathematics see "Vocational Mathematics," by William H. Dooley.
Or multiply the square of diameter by .7854
Or multiply the square of circumference by .07958
Or multiply the square of one-half diameter by 3.1416
To Find Side of an Inscribed Square:
Multiply diameter by .7071
Or multiply circumference by .2251
Or divide circumference by 4.4428
To Find Side of a Square of Equal Area:
Multiply diameter by .8862 Or divide diameter by 1.1284 Or multiply circumference by .2821 Or divide circumference by 3.545
Square:
A side multiplied by 1.4142 equals diameter of its circumscribing circle
A side multiplied by 4.443 equals circumference of its circumscribing circle
A side multiplied by 1.1284 equals diameter of a circle of equal area
A side multiplied by 3.545 equals circumference of an equal circle
To Find the Area of an Ellipse:
Multiply the product of its axes by .7854
Or multiply the product of its semi-axes by 3.14159
Rules Relative to Other Geometrical Figures
Contents of cylinder = area of end X length
Contents of wedge = area triangular base X altitude
Surface of cylinder = length X circumference + area of both ends
Surface of sphere = diameter squared X 3.1416, or = diameter
X circumference Contents of sphere = diameter cubed X .5236 Contents of pyramid or cone, right or oblique, regular or irregular = area of base X one-third altitude
Area of triangle = base X one-half altitude
Area of parallelogram = base X altitude
Area of trapezoid = altitude X one-half the sum of parallel sides
 
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