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

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

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

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

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

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

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

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

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

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 44.125 in2 SA = 88.25 in2 Project Lead The Way, Inc. Copyright 2007