Physical Properties of Geometric Solids

2. Physical Properties of Geometric Solids Calculating Volume, Mass Weight, and Surface Area

3. 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.

4. 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.

5. Metric English System cubiccubic inch centimeter (in3) (cm3) Volume Volume (V) refers to the amount of space occupied by an object or enclosed within a container.

6. 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

7. 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).

8. 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

9. 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

10. Volume of a Cone • The formula for calculating the volume (V) of a coneis: 1.50 2.00

12. Volume of pyramid B = Area of base

13. 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?

14. 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. 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.

15. 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

16. 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

17. 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

19. Surface Area • If one gallon paint covers 3000 square inches. How many parts can be painted with 4 gallons of paint?

20. 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

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! Massis the amount of matter in an object Weightis the force of gravity acting on mass.

23. International System US Customary System gramPounds (lb) (g) 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 massis typically recorded in pounds (force), when it should be recorded in slugs. In the metric system grams is used

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. SI US Newton pound (grams) (lb) 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.

26. 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.

27. weight = massx acceleration due to gravity (pound-force) (pound-mass) (ft/sec2) Mass to Weight Formula (US Customary) W = Mg g = 32.17 ft/sec2 If the mass of an object is 4 lbs, what is the object in weight lbs (force lb)?

28. weight = massx acceleration due to gravity (kg-mass) (meters/sec2) (kg-force) Mass to Weight (SI System ) W = Mg g = 9.8 m/sec2 If the weight of an object is 120 kgs what is its mass in kg.

29. Density • 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 High Density Low Density

30. Weight Density 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

31. Density US Customary pounds per cubic inch (lbs/in3),(tons/mi3), (lbs/ft3), Weight density (Dw)is an object’s weight per unit volume. Mass Density (Dm) is an object’s mass per unit volume. . SI System (g/cm3), (g/mL) and (kg/m3)

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 = VolumeDm = mass density m = mass in grams or kg V = VolumeDm = mass density W = weight in pounds

35. 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 m = 585.3 cm3 x2.71 g/cm3 m = 1586 g = 1.59 kg

36. 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 V= 6 ft3

37. 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?

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

39. 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?