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: