2Geometric Solids Solids are three-dimensional objects. In sketching, two-dimensional shapes are used to create the illusion of three-dimensional solids.
3Properties of SolidsVolume, 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.
4VolumeVolume (V) refers to the amount of three-dimensional space occupied by an object or enclosed within a container.Metric English Systemcubic cubic inchcentimeter(cc)(in.3)
5Volume of a Cube A cube has sides (s) of equal length. The formula for calculating the volume (V) of a cube is:V = s3V= s3V= 4 in. x 4 in. x 4 in.V = 64 in.3
6Volume 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).
7Volume of Rectangular Prism The formula for calculating the volume (V) of a rectangular prism is:V = wdhV= wdhV= 4 in. x 5.25 in. x 2.5 in.V = 52.5 in.3
8V = r2h 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 = r2hV= r2hV= 3.14 x (1.5 in.)2 x 6 in.V = in.3
9MassMass (M) refers to the quantity of matter in an object. It is often confused with the concept of weight in the SI system.SI U S CustomarySystemgram slug(g)
10WeightWeight (W) is the force of gravity acting on an object. It is often confused with the concept of mass in the U S Customary System.SI U S CustomarySystemNewton pound(N) (lb)
11Mass vs. WeightContrary to popular practice, the terms mass and weight are not interchangeable and do not represent the same concept.W = Mgweight = mass x acceleration due to gravity(lbs)(slugs)(ft/sec2)g = ft/sec2
12Mass vs. WeightAn object, whether on the surface of the earth, in orbit, or on the surface of the moon, still has the same mass.However, the weight of the same object will be different in all three instances because the magnitude of gravity is different.
13Mass vs. WeightEach measurement system has fallen prey to erroneous cultural practices.In the SI system, a person’s weight is typically recorded in kilograms when it should be recorded in Newtons.In the U S Customary System, an object’s mass is typically recorded in pounds when it should be recorded in slugs.
14Weight DensityWeight density (WD) is an object’s weight per unit volume.U S Customary Systempounds per cubic inch(lb/in.3)
15Weight Density Substance Weight Density Water Freshwater Seawater GasolineAluminumMachinable WaxHaydite Concrete.036 lb/in.3.039 lb/in.3.024 lb/in.3.098 lb/in.3.034 lb/in.3.058 lb/in.3
16W = VDw Calculating Weight To calculate the weight (W) of any solid, its volume (V) and weight density (Dw) must be known.W = VDwW = VDwW = in.3 x .098 lb/in.3W = 3.6 lb
17Area vs. Surface AreaThere 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.
18Surface 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 = 6ASA = 6ASA = 6 x (4 in. x 4 in.)SA = 96 in.2
19Surface 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 in.2SA = in.2
20Surface 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 = (2r)h + 2(r2)SA = 2(r)h + 2(r2)SA = in in.2SA = in.2