Properties of Geometric Solids © 2012 Project Lead The Way, Inc.Introduction to Engineering Design

Properties of Solids (3D Objects) 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.

Formula Sheet: Volume (enclosed space)

Mass & Weight Mass (M) refers to the quantity of matter in an object. Weight is the force of gravity acting on mass. W = mg weight = mass x acceleration due to gravity (lb) (N) (slugs) (kg) (32.2 ft/sec 2 ) (9.80 m/s 2 )

Density Mass Density (D m ) is an object’s mass per unit volume: D m = M / V g/cm 3 Weight density (D w ) is an object’s weight per unit volume. D w = W / V lb/in 3

Examples of Density MaterialMass Density (g/cm 3 ) Weight Density (lb/in. 3 ) Apples Water (Pure) Water (Sea) Ice Concrete Aluminum Steel (1018) Gold

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.

Surface Area Calculations: SA = (2  r)h + 2(  r 2 ) SA = 6s 2 SA = 2(w×h + w×d + d×h)