## 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.

##### Products & Services
Cutting Tool Inserts
Cutting tool inserts are replaceable attachments for cutting tools. They typically contain the actual cutting edge.
Threading inserts are replaceable cutting inserts that are used to create internal or external threads. They are used typically with a tool holder on a lathe or turning center.
Hydraulic Cylinders
Hydraulic cylinders are actuation devices that utilize pressurized hydraulic fluid to produce linear motion and force.
Dewatering Equipment
Dewatering equipment uses force, including vacuum and centrifugal motion, to separate water from solids.
Surface Metrology Equipment
Surface metrology equipment is used to measure the surface finish and/or geometry of engineering components. Surface texture and topology characteristics include surface roughness, contour, form, waviness, and defects.

##### Topics of Interest

3.1 GEOMETRIC CONSTRUCTION The following figures show the methods used to perform most of the basic geometric constructions used in standard drawing and layout practices. Many of these constructions...

3.1 MENSURATION Plane areas, surface areas, and volumes of the regular geometric shapes and solids illustrated herein can be calculated by using the formulas which appear next to the respective...

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...

Chapter 1: Overview Figure 1.1: Hierarchy of modeling and simulation. Chapter 2: Mathematical Concepts in Modeling Figure 2.1: Frame A and coordinate system ] A. Figure 2.2: Vector triangle.

LEARNING OBJECTIVES After completing this lesson, you will be able to: Draw an Inscribed and Circumscribed Polygon. Create an Ellipse using two different methods. Draw an object called Donut.

Product Announcements
Stanley Engineered Fastening - Spiralock
Sandvik Coromant Co.
Sandvik Coromant Co.