1. Properties of Geometric Solids
Introduction to Engineering Design TM
Unit 1 – Lesson 1.4 – Geometric Shapes and Solids
Project Lead The Way, Inc.
Copyright 2007

2. Properties of Geometric Solids
Introduction to Engineering Design TM
Unit 1 – Lesson 1.4 – Geometric Shapes and Solids
Properties of Geometric Solids
Calculating Volume, Weight, and Surface Area
Project Lead The Way, Inc.
Copyright 2007

3. Properties of Geometric Solids
Introduction to Engineering Design TM
Unit 1 – Lesson 1.4 – Geometric Shapes and Solids
Geometric Solids
Solids are three-dimensional objects.
In sketching, two-dimensional shapes are used to create the illusion of three-dimensional solids.
Project Lead The Way, Inc.
Copyright 2007

4. Properties of Geometric Solids
Introduction to Engineering Design TM
Unit 1 – Lesson 1.4 – Geometric Shapes and 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.
Project Lead The Way, Inc.
Copyright 2007

5. Properties of Geometric Solids
Introduction to Engineering Design TM
Unit 1 – Lesson 1.4 – Geometric Shapes and Solids
Volume
Volume (V) refers to the amount of space occupied by an object or enclosed within a container.
Metric English System
cubic cubic inch
centimeter
(cc)
(in3)
Project Lead The Way, Inc.
Copyright 2007

6. Properties of Geometric Solids
Introduction to Engineering Design TM
Unit 1 – Lesson 1.4 – Geometric Shapes and Solids
Volume of a Cube
A cube has sides (s) of equal length.
The formula for calculating the volume (V) of a cube is:
V = s3
V= s3
V= 4 in x 4 in x 4 in
V = 64 in3
Project Lead The Way, Inc.
Copyright 2007

7. Properties of Geometric Solids
Introduction to Engineering Design TM
Unit 1 – Lesson 1.4 – Geometric Shapes and Solids
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).
Project Lead The Way, Inc.
Copyright 2007

8. Properties of Geometric Solids
Introduction to Engineering Design TM
Unit 1 – Lesson 1.4 – Geometric Shapes and Solids
Volume of a Rectangular Prism
The formula for calculating the volume (V) of a rectangular prism is:
V = wdh
V= wdh
V= 4 in x 5.25 in x 2.5 in
V = 52.5 in3
Project Lead The Way, Inc.
Copyright 2007

9. Properties of Geometric Solids
Introduction to Engineering Design TM
Unit 1 – Lesson 1.4 – Geometric Shapes and Solids
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= 3.14 x (1.5 in)2 x 6 in
V = in3
Project Lead The Way, Inc.
Copyright 2007

10. Properties of Geometric Solids
Introduction to Engineering Design TM
Unit 1 – Lesson 1.4 – Geometric Shapes and Solids
Mass
Mass (M) refers to the quantity of matter in an object. It is often confused with the concept of weight in the metric system.
Metric English System
gram slug
(g)
Project Lead The Way, Inc.
Copyright 2007

11. Properties of Geometric Solids
Introduction to Engineering Design TM
Unit 1 – Lesson 1.4 – Geometric Shapes and Solids
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)
Project Lead The Way, Inc.
Copyright 2007

12. Properties of Geometric Solids
Introduction to Engineering Design TM
Unit 1 – Lesson 1.4 – Geometric Shapes and Solids
Mass vs. Weight
Contrary to popular practice, the terms mass and weight are not interchangeable, and do not represent the same concept.
W = Mg
weight = mass x acceleration due to gravity
(lbs)
(slugs)
(ft/sec2)
g = ft/sec2
Project Lead The Way, Inc.
Copyright 2007

13. Properties of Geometric Solids
Introduction to Engineering Design TM
Unit 1 – Lesson 1.4 – Geometric Shapes and Solids
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.
Project Lead The Way, Inc.
Copyright 2007

14. Properties of Geometric Solids
Introduction to Engineering Design TM
Unit 1 – Lesson 1.4 – Geometric Shapes and Solids
Mass vs. Weight
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.
Project Lead The Way, Inc.
Copyright 2007

15. Properties of Geometric Solids
Introduction to Engineering Design TM
Unit 1 – Lesson 1.4 – Geometric Shapes and Solids
Weight Density
Weight density (WD) is an object’s weight per unit volume.
English System
pounds per cubic inch
(lbs/in3)
Project Lead The Way, Inc.
Copyright 2007

16. Properties of Geometric Solids
Introduction to Engineering Design TM
Unit 1 – Lesson 1.4 – Geometric Shapes and Solids
Weight Density
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
Project Lead The Way, Inc.
Copyright 2007

17. Properties of Geometric Solids
Introduction to Engineering Design TM
Unit 1 – Lesson 1.4 – Geometric Shapes and Solids
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 = in3 x .098 lbs/in3
W = 3.6 lbs
Project Lead The Way, Inc.
Copyright 2007

18. Properties of Geometric Solids
Introduction to Engineering Design TM
Unit 1 – Lesson 1.4 – Geometric Shapes and Solids
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.
Project Lead The Way, Inc.
Copyright 2007

19. Properties of Geometric Solids
Introduction to Engineering Design TM
Unit 1 – Lesson 1.4 – Geometric Shapes and Solids
Surface Area Calculations
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 = 6 x (4 in x 4 in)
SA = 96 in2
Project Lead The Way, Inc.
Copyright 2007

20. Properties of Geometric Solids
Introduction to Engineering Design TM
Unit 1 – Lesson 1.4 – Geometric Shapes and Solids
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 = 2 x in2
SA = in2
Project Lead The Way, Inc.
Copyright 2007

21. Properties of Geometric Solids
Introduction to Engineering Design TM
Unit 1 – Lesson 1.4 – Geometric Shapes and Solids
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 = (2r)h + 2(r2)
SA = 2(r)h + 2(r2)
SA = in in2
SA = in2
Project Lead The Way, Inc.
Copyright 2007