Geoscience Reference
In-Depth Information
2.11.2 r
elevant
g
eometriC
e
quations
Circumference
C
of a circle:
C
= π
d
= 2π
r
Perimeter
P
of a square with side
a
:
P
= 4
a
Perimeter
P
of a rectangle with sides
a
and
b
:
P
= 2
a
+ 2
b
Perimeter
P
of a triangle with sides
a
,
b
, and
c
:
P
=
a
+
b
+
c
Area
A
of a circle with radius
r
(
d
= 2
r
):
A
= π
d
2
/4 = π
r
2
Area
A
of duct in square feet when
d
is in inches:
A
= 0.005454
d
2
Area
A
of a triangle with base
b
and height
h
:
A
= 0.5
bh
Area
A
of a square with sides
a
:
A
=
a
2
Area
A
of a rectangle with sides
a
and
b
:
A
=
ab
Area
A
of an ellipse with major axis
a
and minor axis
b
:
A
= π
ab
Area
A
of a trapezoid with parallel sides
a
and
b
and height
h
:
A
= 0.5(
a
+
b
)
h
Area
A
of a duct in square feet when
d
is in inches:
A
= π
d
2
/576 = 0.005454
d
2
Volume
V
of a sphere with a radius
r
(
d
= 2
r
):
V
= 1.33π
r
3
= 0.1667π
d
3
Volume
V
of a cube with sides
a
:
V
=
a
3
Volume
V
of a rectangular solid (sides
a
and
b
and height
c
):
V
=
abc
Volume
V
of a cylinder with a radius
r
and height
H
:
V
= π
r
2
h
= π
d
2
h
/4
Volume
V
of a pyramid:
V
= 0.33
2.11.3
g
eometriCal
C
alCulations
2.11.3.1 Perimeter and Circumference
On occasion, it may be necessary to determine the distance around grounds or landscapes. To mea-
sure the distance around property, buildings, and basin-like structures, it is necessary to determine
either perimeter or circumference. The
perimeter
is the distance around an object; a border or
outer boundary.
Circumference
is the distance around a circle or circular object, such as a clarifier.
Distance is a linear measurement that defines the distance (or length) along a line. Standard units
of measurement such as inches, feet, yards, and miles and metric units such as centimeters, meters,
and kilometers are used.
The perimeter (
P
) of a rectangle (a four-sided figure with four right angles) is obtained by adding
the lengths (
L
i
) of the four sides (see Figure 2.1):
Perimeter =
L
1
+
L
2
+
L
3
+
L
4
(2.4)
L
1
L
4
L
2
L
3
FIGURE 2.1
Perimeter.
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