1. Properties of Geometric Solids
Introduction to Engineering Design TM
Unit 1 – Lesson 1.4 – Geometric Shapes and Solids
Volume and Surface Area
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
Solids
Solids are three-dimensional objects.
In sketching, two-dimensional shapes are used to create the illusion of three-dimensional solids.
Identify the Shapes in all pictures
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
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

4. 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

5. 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 4”
Per
side
V= s3
V= 4 in x 4 in x 4 in
V = 64 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 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

7. 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

8. 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

9. 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

10. 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