1. Properties of Geometric Solids
Introduction to Engineering Design TM
Unit 1 – Lesson 1.4 – Geometric Shapes and Solids
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2. 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

3. 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
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Copyright 2007

4. 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.
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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
(cm3)
(in3)
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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 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
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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).
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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
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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
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10. Volume of a Cone
The formula for calculating the volume (V) of a cone is:
2.00
1.50

12. Volume of pyramid
B = Area of base

13. 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?
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14. 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.
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15. 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

16. 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(4x x x2.5)
SA = in2
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
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 = in2
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Copyright 2007

19. 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 square inches. How many parts can be painted with 4 gallons of paint?
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Copyright 2007

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

21. 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

22. 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.

23. 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)
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24. 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.

25. 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)
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Copyright 2007

26. 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

27. 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 = 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

28. 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.
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Copyright 2007 28

29. 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

30. 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

31. 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)
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Copyright 2007

32. 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

33. 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

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

35. 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 cm. Aluminum has a mass density of 2.71 g/cm3
m = VDm
V = whd = (3.81 cm)(8.89 cm )(17.28 cm) = 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 = cm3 x g/cm3
m = 1586 g = 1.59 kg

36. 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

37. 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
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Copyright 2007

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

39. 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 kg/mm3 what is the approximated mass of the aluminum part in kg?
Answer is 0.2 KG
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Copyright 2007