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Properties of
Geometric SolidsCalculating Volume,
Weight, and Surface Area
• Solids are three-
dimensional objects.
• In sketching, two-
dimensional shapes are
used to create the illusion
of three-dimensional
solids.
Geometric Solids
Properties of Solids
Volume, mass, weight, density, and
surface area are properties that all solids
possess. These properties are used by
engineers and manufacturers to determine
material type, cost, and other factors
associated with the design of objects.
Volume
Volume (V) refers to the amount of space
occupied by an object or enclosed within a
container.
Metric English System
cubic cubic inchcentimeter
(cc)(in3)
V= s3
V = 64 in3
Volume of a Cube
A cube has sides (s) of
equal length.
The formula for
calculating the volume
(V) of a cube is:
V = s3V= 4 in x 4 in x 4 in
Volume of a Rectangular Prism
A rectangular prism has
at least one side that is
different in length from the
other two.
The sides are identified as
width (w), depth (d), and
height (h).
Volume of a Rectangular Prism
The formula for calculating
the volume (V) of a
rectangular prism is:
V = wdhV= wdh
V = 52.5 in3
V= 4 in x 5.25 in x 2.5 in
Volume of a Cylinder
To calculate the volume
of a cylinder, its radius
(r) and height (h) must be
known.
The formula for
calculating the volume
(V) of a cylinder is:
V = r2h
V= r2h
V = 42.39 in3
V= 3.14 x (1.5 in)2 x 6 in
Mass (M) refers to the quantity of matter in
an object. It is often confused with the
concept of weight in the metric system.
Mass
Metric English System
gram slug(g)
Weight
Weight (W) is the force of gravity acting on
an object. It is often confused with the
concept of mass in the English system.
Metric English System
Newton pound(N) (lb)
Mass vs. Weight
weight = mass x acceleration due to gravity(lbs) (slugs) (ft/sec2)
W = Mg
g = 32.16 ft/sec2
Contrary to popular practice, the terms mass
and weight are not interchangeable, and do
not represent the same concept.
Mass vs. Weight
An object, whether on the surface of the
earth, in orbit, or on the surface of the
moon, still has the same mass.
However, the weight of the same object
will be different in all three instances,
because the magnitude of gravity is
different.
Each measurement system has fallen prey to
erroneous cultural practices.
In the metric system, a person’s weight is
typically recorded in kilograms, when it
should be recorded in Newtons.
In the English system, an object’s mass is
typically recorded in pounds, when it should
be recorded in slugs.
Mass vs. Weight
Weight Density
Weight density (WD) is an object’s weight
per unit volume.
English System
pounds per cubic inch
(lbs/in3)
Substance Weight Density
Water
Freshwater
Seawater
Gasoline
Aluminum
Machinable Wax
Haydite Concrete
.036 lb/in3
.039 lb/in3
.024 lb/in3
.098 lb/in3
.034 lb/in3
.058 lb/in3
Weight Density
Calculating Weight
To calculate the
weight (W) of any
solid, its volume (V)
and weight density
(Dw) must be known.
W = VDw
W = VDw
W = 3.6 lbs
W = 36.75 in3 x .098 lbs/in3
Area vs. Surface Area
There is a distinction between area (A) and
surface area (SA).
Area describes the measure of the two-
dimensional space enclosed by a shape.
Surface area is the sum of all the areas of the
faces of a three-dimensional solid.
In order to calculate the
surface area (SA) of a cube,
the area (A) of any one of its
faces must be known.
The formula for calculating
the surface area (SA) of a
cube is:
SA = 6A
SA = 6A
SA = 96 in2
SA = 6 x (4 in x 4 in)
Surface Area Calculations
In order to calculate the
surface area (SA) of a
rectangular prism, the
area (A) of the three
different faces must be
known.
SA = 2(wd + wh + dh)
SA = 2(wd + wh + dh)
SA = 88.25 in2
SA = 2 x 44.125 in2
Surface Area Calculations
In order to calculate
the surface area (SA)
of a cylinder, the area
of the curved face,
and the combined
area of the circular
faces must be known.
SA = (2r)h + 2(r2)
SA = 2(r)h + 2(r2)
SA = 88.25 in2
SA = 56.52 in2 + 14.13 in2
Surface Area Calculations
Forging the Innovation Generation
Applied Design Process
Design Process Steps
– ITEA Standards for Technological Literacy
Define a Problem
Portable video games provide
entertainment for kids, but they are
expensive and constantly need to be
recharged or new batteries.
A need exists for a simple, inexpensive
toy that does the same thing but does
not use electricity.
Brainstorm
Research & Generate Ideas Product Market Survey
Surveyed by _____________________
Product Description
The Toy Skateboard is a product designed to be safe, fun, and challenging. It is affordable, fits in your pocket, and is unique to each individual. This product is durable and lightweight with a professional finish that you can apply. Kids can learn tricks and stunts just like the full size skateboard. Ramps, rails, and steps are just a few of the accessories that will increase skill levels of ages. The Skateboard is a great way to challenge your friends and have fun.
Please answer the following questions as honestly and completely as possible.
Male _____
Female _____
Elementary _____
Junior High _____
High School _____
Adult _____
Do you feel this product is marketable?
Yes _____
No _____
Would you buy this product?
Yes _____
No _____
How much would you expect to pay for this product?
$2-$4 _____
$4-$6 _____
$6-$8 _____
$8-$10 _____
What improvements would you suggest?
Size _____
Shape _____
Finish _____
Materials _____
Other _____
Thank you for your time and cooperation.
Identify Criteria & Specify ConstraintsClient: World Industries
Target Consumer: Parents (purchasers) and Children-age 9-15 (end users)
Problem Statement: Portable video games provide entertainment for kids, but they are expensive and
constantly need recharged or new batteries.
A need exists for a simple, inexpensive toy that does the same thing but does not use
electricity.
Design Statement: Design, market, test, and mass produce a multi-skill educational toy that is challenging
and fun.
Constraints: Fits in pocket
Inexpensive
Competitive
Develop skill
Variety of shapes
No electricity
Variety of materials
Explore Possibilities
Select an Approach
Develop a Design Proposal
Make a Model or Prototype
Test & Evaluate Design Using
Specifications
Refine the Design
1. Add rough surface to top of board for
better grip.
2. Make board in flat and rectangular
shapes for different applications.
3. Make wheels using hard and soft
compounds for different applications.
Create or Make Solution
Communicate Processes or Results
References
Madsen, D., Folkestad, J., Schertz, K., Shumaker, T., Stark, C., & Turpin, J. (2004). Engineering Drawing and Design (3rd ed.). Albany, NY: Thompson Learning, Inc. / Delmar.
Writer: Gary Platt
Content Editors: Sam Cox & Wes Terrell
Production Work: C.J. Amarosa
Credits
Isometric Cubes
Step 4
30°30°
Step 3
Isometric Circles & Curves
Step 1 Step 2
Isometric Circles & Curves
Step 3 Step 4
Isometric Circles & Curves
Step 5 Step 6
3D Sketching Techniques
Boxing in the Sketch
3D Sketching Techniques
Boxing in the Sketch
3D Sketching Techniques
Isometric Grid Paper
3D Sketching Techniques
Notes
Annotations
Title
Signature
Date
Description
Label
Oblique Cube - Cavalier
Oblique Cube - Cabinet
One Point Perspective
Two Point Perspective
Pictorial Drawing
Disadvantages
Create foreshortened views
Do not allow for accurate prototyping
Orthographic
(Multiview Drawings)
Orthographic - Principal Views
Orthographic - View Selection
Characteristics for selecting the front view
Best shape & details
Longest dimensions
Fewest hidden lines
Most natural position or use of object
Most stable position
Relationship of other views
Precedence of Lines
Object lines exist over hidden and center lines
Hidden lines exist over center lines
Cutting plane lines exist over center lines
Precedence of LinesExample 1
Object line over hidden lines
Example 2Object line
over center line
References:
Bertoline, G.R., & Wiebe, E.N. (2003). Technical graphics communication (3rd ed.). Burr Ridge, Illinois: McGraw- Hill. Madeson, D.A., Folkestad, J., Schertz, K.A., & Shumaker, T.M. (2004). Engineering drawing and design (3rd ed.).
Albany, NY: Delmar Publishers.Walker, J.R. & Mathis B.D.(2007). Exploring drafting(10th ed.). Tinley Park, IL: Goodheart-Willcox Publisher.
Writer: Matt Putman
Content Editor: Wes Terrell & Sam Cox
Production Work: C.J. Amarosa
Credits:
Dimensioning Guidelines
Lesson Topics• Extension & Dimension Line
Conventions
• Guidelines for Locating Dimensions
• Leader Line Conventions
• Other Common Dimensioning Errors
Extension & Dimension Line Conventions
• Dimension Line Definition
• Dimension Line Geometry
• Unidirectional Dimensions
• Extension Line Definition
• Extension Line Geometry
Dimension LineTerminology
A dimension lineis a thin line drawn perpendicular to extension lines with arrowheads at each end.• indicates linear
distance between object edges or features
Dimension line arrows are approximately
1/16” wide by 3/16” long. The first
dimension occurs about 3/8” from the
object, with each successive dimension
spaced ¼” apart.
Dimension Line Geometry
All dimension values should be oriented
parallel to the bottom edge of the paper,
and should read left-to-right (unidirectional).
Unidirectional Dimensions
Incorrect
All dimension values should be oriented
parallel to the bottom edge of the paper,
and should read left-to-right (unidirectional).
Unidirectional Dimensions
Correct
TerminologyExtension Line
An extension line is a thin solid line that occurs perpendicular to a dimension line.• extends an object
line or centerline
• shows the extents of a dimension
Extension lines start about 1/16” from the
object, and extend about 1/8” past the last
dimension.
Extension Line Geometry
18
116
Object
Do not use an object line as an extension
line. Dimensions lines must terminate on
extension lines.
Object Lines as Extension
Lines
Incorrect
Guidelines forLocating Dimensions
• Dimension Placement
• Contour Dimensioning
• Centering Dimension Values
• Dimensioning Between Views
• Dimensioning Within an Object
• Dimensioning Through an Object
• Crossing Extension Lines
• Crossing Dimension Lines
If properly placed, dimensions will appear
to taper from large to small. The largest
dimensions should occur furthest away
from the object.
Dimension Placement
Dimensions should be placed on the view that best illustrates the shape or contour of the feature.
Contour Dimensioning
Incorrect
Dimensions should be placed on the view that best illustrates the shape or contour of the feature.
Contour Dimensioning
Correct
In most cases, dimension values should be
centered on their dimension lines or
between their extension lines.
Centering Dimension Values
Incorrect
Whenever possible, place dimensions in
the space between the front, right side, and
top views.
Dimensioning Between Views
Incorrect
Do not place dimensions within the object.
Always locate dimensions outside of the
object.
Dimensioning Within an
Object
Incorrect
Whenever possible, avoid sending an
extension line through an object view.
Dimensioning Through an Object
Incorrect
Whenever possible, avoid crossing
extension lines.
Crossing Extension Lines
Incorrect
Never cross a dimension line with another dimension line or an extension line.
Crossing Dimension Lines
Incorrect
Leader Line Conventions
• Leader Line Definition
• Leader Line Angles
• Diameter versus Radius
• Hole and Cylinder Dimensions
TerminologyLeader Line
• points toward the center of the feature
• arrow on one end touches the part or detail
• text is extended from a short horizontal line or “shoulder” on the other end
A leader line is a thin, solid line used to indicate the feature with which a dimension, note, or symbol is associated.
Whenever possible, a leader line dimension should occur at approximately 30°, 45°, or 60° from the horizontal or vertical.
Leader Line Angles
A complete circular object is called out by
its diameter. A fillet or round is identified by
its arc radius.
Diameter versus Radius
A hole is dimensioned on a circular view
using a leader line. A cylinder, or solid
cylindrical feature, is dimensioned on a
side view using a linear dimension.
Hole and Cylinder Dimensions
Other Common Dimensioning Errors
• Unnecessary Dimensions
• Duplicate Dimensions
• Dimensioning to Hidden Lines
• True Scale
Avoid unnecessary dimensions. A drawing
must contain only those dimensions that are
necessary to define the object’s geometry.
Unnecessary Dimensions
Incorrect
Do not call out the same dimension on a
different view.
Duplicate Dimensions
Incorrect
Avoid dimensioning to hidden lines. If
necessary, generate an alternate view, or
section view, where the feature appears as
an object line.
Dimensioning to Hidden Lines
Dimensions should reflect an object’s
actual size; not its scaled size.
True Scale
Bertoline, G. R., & Wiebe, E. N. (2003). Technical graphics communication (3rd ed.). NY: McGraw-Hill Companies, Inc.
Lockhart, S., & Johnson, C. (2000). Engineering design communication. Upper Saddle River, NJ: Prentice Hall Inc.
Madsen D. A., Folkestad, J., Schertz, K. A., Shumaker, T. M., Stark, C., & Turpin, J. L. (2004). Engineering drawing and design (3rd ed.). Albany, NY: Delmar-Thompson Learning.
Spence, W. P. (1991). Drafting technology and practice (3rd ed.). NY: Glencoe-McGraw Hill Inc.
Wallach, P. (2003). Fundamental of modern drafting.Clifton Park, NY: Thomson Delmar Learning.
References
Writer: Terry C. Nagy Jr.
Lesson Editor: Ed Hughes
Narration: CJ Amarosa
Production: CJ Amarosa
Credits: