Handbook of Machining and Metalworking Calculations
With easy-to-use tables, charts, listings, and formulas, this convenient hands-on resource will help you solve virtually any problem involving metalworking and machining tools and applications.
TABLE OF CONTENTS Handbook of Machining and Metalworking Calculations
Chapter 2: Mensuration of Plane and Solid Figures
2.1 MENSURATION
Mensuration is the mathematical name for calculating the areas, volumes, length of sides, and other geometric parts of standard geometric shapes such as circles, spheres, polygons, prisms, cylinders, cones, etc., through the use of mathematical equations or formulas. Included here are the most frequently used and important mensuration formulas for the common geometric figures, both plane and solid. (See Figs. 2.1 through 2.36.)
| Symbols |
|
| A | area |
| a, b, etc. | sides |
| A, B, C | angles |
| h | height perpendicular to base b |
| L | length of side or edge |
| r | radius |
| n | number of sides |
| C | circumference |
| V | volume |
| S | surface area |
Figure 2.1: Oblique triangle.
Figure 2.2: Oblique triangle.
Figure 2.3: Rectangle.
Figure 2.4: Parallelogram.
Figure 2.5: Rhombus.
Figure 2.6: Trapezoid.
Figure 2.7: Polyhedra.
Figure 2.8: Trapezium.
Figure 2.9: Regular polygon.
Figure 2.10: Inscribed circle.
Figure 2.11: Circumscribed circle.
Figure 2.12: Inscribed polygon.
Figure 2.13: Circumscribed polygon.
Figure 2.14: Circle circumference.
Figure 2.15: Circle area.
Figure 2.16: Length of arc.
Figure 2.17: Chord and sector.
Figure 2.18: Segment of a circle.
Figure 2.19: Ring.
Figure 2.20: Ellipse.
Figure 2.21: Pyramid.
Figure 2.22: Sphere.
Figure 2.23: Cylinder.
Figure 2.24: Cone.
Figure 2.25: Spherical segment.
Figure 2.26: Frustum of a cone.
Figure 2.27: Truncated cylinder.
Figure 2.28: Spherical zone.
Figure 2.29: Spherical wedge.
Figure 2.30: Paraboloid.
Figure 2.31: Spherical sector.
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