Transcript MATH 2160 1st Exam Review - Valdosta State University

Perimeter, Area, and
Volume
Geometry
and
Measurement
Measurement

5 ft
Rectangle
3 ft
Perimeter
 P = 2l + 2w, where l = length and
w = width
 Example: l = 5 ft and w = 3 ft


P rectangle
=

P
=
2(5 ft) + 2(3 ft)
P
P
=
=
10 ft + 6 ft
16 ft

2l + 2w
Measurement

5 ft
Rectangle
3 ft
Area
 A = lw where l = length and w =
width
 Example: l = 5 ft and w = 3 ft


A rectangle = lw

A
=
(5 ft)(3 ft)

A
=
15 ft2
Measurement

Square
3 ft
Perimeter
 P = 4s, where s = length of a side
 Example: s = 3 ft


P square
=

P
=
4(3 ft)

P
=
12 ft
4s
Measurement

Square
3 ft
Area
 A = s2 where s = length of a side
 Example: s = 3 ft


A square =
s2

A
=
(3 ft)2

A
=
9 ft2
Measurement

Triangle
Perimeter
 P = a + b + c, where a, b, and c
are the lengths of the sides of the
triangle
 Example: a = 3 m; b = 4 m; c = 5
m

P triangle
P
=
P
=

=
a+b+c
3m+4m+5m
12 m
Measurement

Triangle
4m
5m
3m
Area
 A = ½ bh, where b is the base and
h is the height of the triangle
 Example: b = 3 m; h = 4 m

A triangle =
A
=
A
=

½ bh
½ (3 m) (4 m)
6 m2
Measurement

3 cm
Circle
Circumference
 C circle = d or C = 2r, where d =
diameter and r = radius


Example: r = 3 cm

C circle =
2r

C
=
2(3 cm)

C
=
6 cm
Measurement

3 cm
Circle
Area
 A = r2, where r = radius


Example: r = 3 cm
r2

A circle
=

A
=
(3 cm)2

A
=
9 cm2
Measurement

Rectangular Prism
7 cm
5 cm
Volume:
6 cm
 V = lwh where l is length; w is width;
and h is height
 Example: l = 6 cm; w = 5 cm; h = 7 cm


V rectangular prism = Bh = lwh

V
=
(6 cm)(5 cm)(7 cm)

V
=
210 cm3
Measurement

Cube
5 cm
Volume:
 V = s3 where s is the length of a side
 Example: s = 5 cm


V cube = Bh = s3

V
=
(5 cm)3

V
=
125 cm3
Measurement
7m
5m

Triangular Prism
6m
Volume:
 V = ½ bhl where b is the base; h is
height of the triangle; and l is length of
the prism
 Example: b = 6 m; h = 5 m; l = 7 m


V triangular prism = Bh = ½ bhl

V
=
½ (6 m)(5 m)(7 m)

V
=
105 m3
3 ft
Measurement
12 ft

Cylinder
Volume of a Cylinder: V = r2h
where r is the radius of the base
(circle) and h is the height.
 Example: r = 3 ft and h = 12 ft.
 V cylinder =
Bh = r2h
 V
=
(3 ft)2  (12 ft)
 V
=
(9 ft2)(12 ft)
 V
=
108 ft3

13 ft
12 ft
Measurement
5 ft

Cone
Volume: V = r2h/3 where r is the
radius of the base (circle) and h is the
height.
 Example: r = 5 ft; h = 12 ft
 V cone=
r2h/3
 V
=
[(5 ft)2  12 ft ]/ 3
 V
=
[(25 ft2)(12 ft)]/3
 V
=
(25 ft2)(4 ft)
 V
=
100 ft3

6 mm
Measurement

Sphere
Volume of a Sphere: V = (4/3) r3
where r is the radius
 Example: r = 6 mm
 V sphere =
4r3/3
 V
=
[4 x (6 mm)3]/3
 V
=
[4 x 216 mm3]/3
 V
=
[864 mm3]/3
 V
=
288 mm3

Measurement

Triangular
Pyramid


Bh
V
3
Square Pyramid
Bh
V
3