Properties of Geometric Solids Calculating Volume, Weight, and Surface Area

Solids are three- dimensional objects. In sketching, two- dimensional shapes are used to create the illusion of three-dimensional solids. Geometric 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.

Volume Volume (V) refers to the amount of space occupied by an object or enclosed within a container. MetricEnglish System cubiccubic inch centimeter (cc) (in 3 )

V= s 3 V = 64 in 3 Volume of a Cube A cube has sides (s) of equal length. The formula for calculating the volume (V) of a cube is: V = s 3 V= 4 in x 4 in x 4 in

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).

Volume of a Rectangular Prism The formula for calculating the volume (V) of a rectangular prism is: V = wdh V = 52.5 in 3 V= 4 in x 5.25 in x 2.5 in

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 =  r 2 h V = in 3 V= 3.14 x (1.5 in) 2 x 6 in

Mass (M) refers to the quantity of matter in an object. It is often confused with the concept of weight in the metric system. Mass MetricEnglish System gramslug (g) (g)

Weight Weight (W) is the force of gravity acting on an object. It is often confused with the concept of mass in the English system. MetricEnglish System Newtonpound (N) (lb) (N) (lb)

Mass vs. Weight weight = mass x acceleration due to gravity (lbs)(slugs)(ft/sec 2 ) W = Mg g = ft/sec 2 Contrary to popular practice, the terms mass and weight are not interchangeable, and do not represent the same concept.

Mass vs. Weight An 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.

Each measurement system has fallen prey to erroneous cultural practices. In the metric system, a person’s weight is typically recorded in kilograms, when it should be recorded in Newtons. In the English system, an object’s mass is typically recorded in pounds, when it should be recorded in slugs. Mass vs. Weight

Weight Density Weight density (W D ) is an object’s weight per unit volume. English System pounds per cubic inch (lbs/in 3 )

Substance Weight Density Water Freshwater Seawater Gasoline Aluminum Machinable Wax Haydite Concrete.036 lb/in lb/in lb/in lb/in lb/in lb/in 3 Weight Density

Calculating Weight To calculate the weight (W) of any solid, its volume (V) and weight density (D w ) must be known. W = VD w W = 3.6 lbs W = in 3 x.098 lbs/in 3

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.

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 = 96 in 2 SA = 6 x (4 in x 4 in) 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 = in 2 SA = 2 x in 2 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(  r 2 ) SA = 2(  r)h + 2(  r 2 ) SA = in 2 SA = in in 2 Surface Area Calculations