Volume and Surface Area Solids Solids are threedimensional

Volume and Surface Area

Solids • Solids are threedimensional objects. • In sketching, twodimensional shapes are used to create the illusion of three-dimensional 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 (V) refers to the amount of space occupied by an object or enclosed within a container. Metric cubic centimeter (cc) English System cubic inch (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= 3 s 4” Per side V= s 3 V= 4 in x 4 in V = 64 in 3

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= 4 in x 5. 25 in x 2. 5 in V = 52. 5 in 3

Area vs. Surface Area There is a distinction between area (A) and surface area (SA). Area describes the measure of the twodimensional space enclosed by a shape. Surface area is the sum of all the areas of the faces of a three-dimensional solid.

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 SA = 6 A cube is: SA = 6 x (4 in x 4 in) SA = 6 A SA = 96 in 2

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 x 44. 125 in 2 SA = 88. 25 in 2