Properties of
Geometric Solids
Calculating Volume,
Weight, and Surface Area
Geometric 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
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
(in3)
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
V= s3
V= 4 in x 4 in x 4 in
V = 64 in3
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= wdh
V= 4 in x 5.25 in x 2.5 in
V = 52.5 in3
Volume of a Cylinder
To calculate the volume
of a cylinder, its radius
(r) and height (h) must be
known.
The formula for
2h
V=
r
calculating the volume
2 x 6 in
V=
3.14
x
(1.5
in)
(V) of a cylinder is:
V = r2h
V = 42.39 in3
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.
Metric English System
gram
slug
(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.
Metric English System
Newton
pound
(N)
(lb)
Mass vs. Weight
Contrary to popular practice, the terms mass
and weight are not interchangeable, and do
not represent the same concept.
W = Mg
weight = mass x acceleration due to gravity
(lbs) (slugs)
(ft/sec2)
g = 32.16 ft/sec2
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.
Weight Density
Substance
Water
Freshwater
Seawater
Gasoline
Aluminum
Machinable Wax
Haydite Concrete
Weight Density
.036 lb/in3
.039 lb/in3
.024 lb/in3
.098 lb/in3
.034 lb/in3
.058 lb/in3
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 = 6A
cube is:
SA = 6 x (4 in x 4 in)
SA = 6A
SA = 96 in2
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
Surface Area Calculations
In order to calculate
the surface area (SA)
of a cylinder, the area
of the curved face,
and the combined
2)
SA
=
2(r)h
+
2(r
area of the circular
2 + 14.13 in2
SA
=
56.52
in
faces must be known.
SA = (2r)h + 2(r2)
SA = 88.25 in2