BOOK_CONTENT
From Handbook of Machining and Metalworking Calculations

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.
Copyright The McGraw-Hill Companies, Inc. 2001 under license agreement with Books24x7

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Topics of Interest

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Learning Objectives After completing this lesson, you will be able to: Draw an Inscribed or Circumscribed Polygon Create an Ellipse using two different methods Define an Elliptical Arc Create...

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