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Volume and Surface Area

Explore the properties and formulas for calculating volume and surface area of various solid shapes like cubes and rectangular prisms. Learn how these measurements are crucial in engineering and design processes.

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Volume and Surface Area

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  1. Volume and Surface Area

  2. 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 4” Per side 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. 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.

  9. 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

  10. 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

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