MATH 2160 1st Exam Review - Valdosta State University
Download
Report
Transcript MATH 2160 1st Exam Review - Valdosta State University
MATH 3190
Surface Area
and
Volume
7 cm
Measurement
Rectangular Prism
5 cm
6 cm
Surface Area: sum of the areas of all of the
faces
Example: There are 4 lateral faces: 2 lateral
faces are 6 cm by 7 cm (A1= wh) and 2
lateral faces are 5 cm by 7 cm (A2 = lh).
There are 2 bases 6 cm by 5 cm (A3 = lw)
A1 = (6 cm)(7 cm) = 42 cm2
A2 = (5 cm)(7 cm) = 35 cm2
A3 = (6 cm)(5 cm) = 30 cm2
SA rectangular prism = 2wh + 2lh + 2lw
SA = 2(42 cm2) + 2(35 cm2) + 2(30 cm2)
SA = 84 cm2 + 70 cm2 + 60 cm2
SA = 214 cm2
Measurement
Cube
5 cm
Surface Area: sum of the areas of all
6 congruent faces
Example: There are 6 faces: 5 cm by
5 cm (A = s2)
SA cube = 6A = 6s2
SA = 6(5 cm)2
SA = 6(25 cm2)
SA = 150 cm2
Measurement
7m
5m
Triangular Prism
Surface Area: sum of the areas of all of the
faces
Example: There are 3 lateral faces: 6 m by
7 m (A1= bl). There are 2 bases: 6 m for the
base and 5 m for the height (2A2 = bh).
A1 = (6 m)(7 m) = 42 m2
2A2 = (6 m)(5 m) = 30 m2
SA triangular prism = bh + 3bl
SA = 30 m2 + 3(42 m2)
SA = 30 m2 + 126 m2
SA = 156 m2
6m
3 ft
Measurement
12 ft
Cylinder
Surface Area: area of the circles plus
the area of the lateral face
Example: r = 3 ft; h = 12 ft
2rh +2r2
SA cylinder=
SA = 2 (3 ft)(12 ft) + 2 (3 ft)2
SA
SA
SA
=
=
=
72 ft2 + 2 (9 ft2)
72 ft2 + 18 ft2
90 ft2
13 ft
12 ft
Measurement
5 ft
Cone
Surface Area: area of the circle plus
the area of the lateral face
Example: r = 5 ft; t = 13 ft
rt +r2
SA cone=
SA = (5 ft)(13 ft) + (5 ft)2
SA
SA
SA
=
=
=
65 ft2 + (25 ft2)
65 ft2 + 25 ft2
90 ft2
8 mm
Measurement
Sphere
Surface Area: 4r2 where r is the
radius
Example: r = 8 mm
SA sphere =
4r2
SA
=
4(8 mm)2
SA
=
4(64 mm2)
SA
=
256 mm2
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 =
4r3/3
V
=
[4 x (6 mm)3]/3
V
=
[4 x 216 mm3]/3
V
=
[864 mm3]/3
V
=
288 mm3
Measurement
Triangular Pyramid
Square Pyramid
Test Taking Tips
Get a good nights rest before
the exam
Prepare materials for exam in
advance (scratch paper, pencil,
and calculator)
Read questions carefully and
ask if you have a question
DURING the exam
Remember: If you are prepared,
you need not fear