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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