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

Properties of Geometric Solids Introduction to Engineering Design TM Unit 1 – Lesson 1.4 – Geometric Shapes and Solids Physical Properties of Geometric Solids Calculating Volume, Mass Weight, 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 Geometric Solids Solids (forms, models, parts) are three-dimensional forms with a surface and provides information about the surface, the surface area, volume, weight, mass and density. In sketching, two-dimensional shapes are used to create the illusion of three-dimensional solids. Wireframe models you can not find surface area, volume, weight , mass and desity 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 Physical 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 (cm3) (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 of equal length (L). The formula for calculating the volume (V) of a cube is: V = L3 V= L3 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 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 = 42.39 in3 Project Lead The Way, Inc. Copyright 2007

Volume of a Cone The formula for calculating the volume (V) of a cone is:   2.00 1.50    

Volume of pyramid B = Area of base

Properties of Geometric Solids Introduction to Engineering Design TM Unit 1 – Lesson 1.4 – Geometric Shapes and Solids volume The part to the right is shelled out and filled with sand. Each bag of sand is 84 cubic inches. What percent of the bag of sand is needed to fill up the part? Project Lead The Way, Inc. Copyright 2007

Properties of Geometric Solids Area vs. Surface Area Introduction to Engineering Design TM Unit 1 – Lesson 1.4 – Geometric Shapes and Solids 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. Measured in square units (units2 , mm2 , in2) Surface are is used to figure out how much cardboard is used is needed to make a package or paint need to paint a car. 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 = 6s2 SA = 6s2 SA = 6 x 42 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(4x5.25 + 4x2.5 + 5.25x2.5) SA = 88.25 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 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 = 2(x1.5)6 + 2(x1.52) SA = 70.65 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 If one gallon paint covers 3000 square inches. How many parts can be painted with 4 gallons of paint? Project Lead The Way, Inc. Copyright 2007

The Prototype below has a total volume of. 31875 cubic meters The Prototype below has a total volume of .31875 cubic meters. What is the side length of a single cube The answer is .233 m

What is the best estimate for the volume of the water in graduated cylinder shown? 43.0 mL 43.5 mL 44.0 mL The answer is 43.0

Are mass and weight the same? NO! Mass is the amount of matter in an object Weight is the force of gravity acting on mass.

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. Matter –Is the amount of stuff in an object. It is defined as anything that has mass and volume. Atoms are composed of matter. Matter is everything around you from the air you breath, to the phone you touch, to the water you drink In the US customary system, an object’s mass is typically recorded in pounds (force), when it should be recorded in slugs. In the metric system grams is used US customary system - English system, imperial system, British system International system – SI system , metric system Volume is space so if you have Styrofoam or wood. They might take up the same space so they could have the same volume. But there is more matter in wood then in Styrofoam International System US Customary System gram Pounds (lb) (g) Project Lead The Way, Inc. Copyright 2007

Volume vs Mass Volume is the amount of space an object takes up. The three balls can have the same volume. But their masses is all different. Since the bowling bowl is the heaviest it has the most stuff in it. It has the most mass. The balloon has the least stuff in it because it is the lightest. It has the least mass.

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’s mass. The force of gravity can be stronger or weaker depending on the situation. Therefore you weight can change in different situation. In the metric system (International System of units “SI”), a person’s weight is typically recorded in grams (mass), when it should be recorded in Newtons. 'pound weight' which was libra pondo in Latin so that is where LB comes from SI US Newton pound (grams) (lb) 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 Mass vs. Weight An object, whether on the surface of the earth, or on the surface of the moon, still has the same mass. There is the same amount of stuff in both objects. However, the weight of the same object will be different on the moon and in space. A person at the beach will not weigh the same as on a mountain. But the person will have the same mass. 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 Mass to Weight Formula (US Customary) W = Mg weight = mass x acceleration due to gravity (pound-force) (pound-mass) (ft/sec2) g = 32.17 ft/sec2 If the mass of an object is 4 lbs, what is the object in weight lbs (force lb)? Project Lead The Way, Inc. Copyright 2007

W = Mg Mass to Weight (SI System ) Properties of Geometric Solids Introduction to Engineering Design TM Unit 1 – Lesson 1.4 – Geometric Shapes and Solids Mass to Weight (SI System ) W = Mg weight = mass x acceleration due to gravity (kg-force) (kg-mass) (meters/sec2) g = 9.8 m/sec2 If the weight of an object is 120 kgs what is its mass in kg. Project Lead The Way, Inc. Copyright 2007 28

Density Presentation Name Course Name Unit # – Lesson #.# – Lesson Name Density is a measure of the amount of matter per unit of volume Gold Wood Objects more dense than water sink Objects less dense than water float Think about identically sized samples of steel and Styrofoam—for instance small cubes the size of the wooden cubes used for the puzzle cube. Which is more dense? Steel or Styrofoam? High Density Low Density

Properties of Geometric Solids Weight Density Introduction to Engineering Design TM Unit 1 – Lesson 1.4 – Geometric Shapes and Solids Density is how much weight (or mass) one cube has. Example: A certain rubber has a density of 15 lbs/ft3. So a one foot by one foot by one foot cube of salt would weigh 15 lbs Weight Density =Dw = weight/Volume Mass Density = Dm mass/Volume Project Lead The Way, Inc. Copyright 2007

Properties of Geometric Solids Density Introduction to Engineering Design TM Unit 1 – Lesson 1.4 – Geometric Shapes and Solids Weight density (Dw) is an object’s weight per unit volume. US Customary pounds per cubic inch (lbs/in3),(tons/mi3), (lbs/ft3), Mass Density (Dm) is an object’s mass per unit volume. . SI System (g/cm3), (g/mL) and (kg/m3) Project Lead The Way, Inc. Copyright 2007

Density Organize each of the ten materials from lightest to heaviest. Then take a guess of the weight of a cubic foot of each material. That is called density. Aluminum Freshwater Silver Air Steel Gasoline Seawater Platinum Gold Milk

Density Air 0.1 (one tenth of one lb/ft3) Gasoline 41 lb/ft3 Freshwater 62 lb/ft3 Milk 64 lb/ft3 Seawater 67 lb/ft3 Aluminum 169 lb/ft3 Steel 484 lb/ft3 Silver 657 lb/ft3 Gold 1,210 lb/ft3 Platinum 1,330 lb/ft3

formulas V = Volume Dm = mass density m = mass in grams or kg W = weight in pounds

m = VDm Calculating Mass Presentation Name Course Name Unit # – Lesson #.# – Lesson Name Calculating Mass Find the mass of an aluminum rectangular prism with the dimensions of 3.81 cm by 8.89 cm by 17.28 cm. Aluminum has a mass density of 2.71 g/cm3 m = VDm V = whd = (3.81 cm)(8.89 cm )(17.28 cm) = 585.3 cm3 m = VDm A note about precision: Since the measured values on which the calculation of the mass is based are recorded to three significant figures and the mass calculation involves multiplication, it is appropriate to round the resulting answer to three significant figures. m = 585.3 cm3 x 2.71 g/cm3 m = 1586 g = 1.59 kg

W = VDw Calculating Weight 15 lbs = V x 2.5 lb/ft3 15 = V·2.5 V= 6 ft3 Presentation Name Course Name Unit # – Lesson #.# – Lesson Name Calculating Weight The weight of cylinder is 15 lbs and has a density of 2.5 lbs per ft3 . What is its volume? W = VDw 15 lbs = V x 2.5 lb/ft3 15 = V·2.5 Does the calculated weight of the aluminum bar make sense in terms of the mass just calculated? Justify your answer. V= 6 ft3

Properties of Geometric Solids Introduction to Engineering Design TM Unit 1 – Lesson 1.4 – Geometric Shapes and Solids A ring made of metal has a mass of 210 grams. You drop a ring into the graduated cylinder with 70 mL of water and the total volume rises to 120 mL. What is the density of the object in g/mL? Answer 4.2 g/mL Project Lead The Way, Inc. Copyright 2007

center of gravity The center of gravity is the average location of the weight of an object.

Properties of Geometric Solids Introduction to Engineering Design TM Unit 1 – Lesson 1.4 – Geometric Shapes and Solids The physical properties generated are for a lead part in CAD. If the material is changed to aluminum with a density 0.000002 kg/mm3 what is the approximated mass of the aluminum part in kg? Answer is 0.2 KG Project Lead The Way, Inc. Copyright 2007