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# Properties of Geometric Solids

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by

## Jon Jarrett

on 10 October 2017

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#### Transcript of Properties of Geometric Solids

SA
V
Properties of
Geometric Solids
Solids are three-dimensional objects.
In sketching, two-dimensional shapes are used to create the illusion of three-dimensional solids.
Geometric 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= s
V= 4 in x 4 in x 4 in
V = 64 in
Volume of a Cube
A cube has sides (s) of equal length.

The formula for calculating the volume (V) of a cube is:
V = s
3
3
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).
V= 3.14r h
V= 3.14 x (1.5 in)2 x 6 in
V = 42.39 in
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
V = wdh
3
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:
2
3
M
Mass
vs.
W
Weight
Mass
(
M
) refers to the quantity of matter (stuff) in an object. It is often confused with the concept of weight.
Mass
Metric English System
gram slug

(g)
Weight
(
W
) is the force of gravity acting on an object. It is often confused with the concept of mass.
Weight
Metric English System
Newton Pound

(N)
Mass vs. Weight
Contrary to popular practice, the terms
mass
and
weight
are not interchangeable, and do not represent the same concept.
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
.

The
weight
of that same object will be different in all three instances, because the force of gravity is different.
Calculating Mass
Weight

density
(
Wd
)

is an object’s weight (force) per unit volume.
Weight Density
English System
pounds per cubic inch
(lbs/in3)
(lbs/in. )
Calculating Weight
Surface Area
Area vs. Surface Area
Surface Area Calculations
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.
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 = 6 x (4 in x 4 in)
SA = 96 in
2
SA = 2(wd + wh + dh)
SA = 2 x 44.125 in
SA = 88.25 in
SA = (2 r)h + 2( r )
SA = 56.52 in + 14.13 in
SA = 88.25 in
SA = 6A
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.
2
SA = 2(wd + wh + dh)
2
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.
Surface Area Calculations
2
2
SA = (2 r)h + 2( r )
2
2
2
2
SA = (2 r)h + 2( r )
SA = 6A
SA = 2(wd + wh + dh)
SA = r h
2
W = VWd
Volume
Volume
(
V
) refers to the amount of three-dimensional space occupied by an object or enclosed within a container.
Metric English System
cubic centimeter cubic inch

(cc)

(in. )
3

(lbs)
When an object is placed on a digital scale, the scale is measuring the force of the object and calculates mass.
W = VD
weight = volume x weight density
When an object is placed on a triple beam balance scale, the scale is measuring the mass because the force on both sides of the beam is equal.
2
W
(in. )
(lbs)
3
V =  r h
3
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