Properties of Geometric Solids

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

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

3. 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.

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

5. Volume of a Cube A cube has sides (s) of equal length. The formula for calculating the volume (V) of a cube is: V = s3 V= s3 V= 4 in x 4 in x 4 in V = 64 in3

6. 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).

7. 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

8. 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

9. Metric English System gram slug (g) Mass Mass (M) refers to the quantity of matter in an object. It is often confused with the concept of weight in the metric system.

10. Metric English System Newton pound (N) (lb) 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.

11. weight = massx acceleration due to gravity (lbs) (slugs) (ft/sec2) Mass vs. Weight Contrary to popular practice, the termsmassand weight are not interchangeable, and do not represent the same concept. W = Mg g = 32.16 ft/sec2

12. 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.

13. Substance Weight Density Water Freshwater Seawater Gasoline Aluminum Machinable Wax Haydite Concrete .036 lb/in3 .039 lb/in3 .024 lb/in3 .098 lb/in3 .034 lb/in3 .058 lb/in3 Weight Density

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.

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 = 6A SA = 6A SA = 6 x (4 in x 4 in) 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 x 44.125 in2 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 = 56.52 in2 + 14.13 in2 SA = 88.25 in2