Name
Date
Chapter 9
Application
Activity
Period
Packaging a Volume
9
Package designers must consider not only the volume of what they need to
pack, but the surface area of the package. The surface area of a package is
the sum of the areas of all the faces of the package. Package designers often
need to find the smallest surface area for a given volume.
You already know that you can use the formula V = e3 to find the volume
of a cube and the formula V = lwh to find the volume of a rectangular
prism. You also know that you can use A = e2 (or A = lw) to find the area of
a square or rectangle.
1
2
4
2
2
The volume of this solid is 23 = 8 cubic units.
The surface area of this solid is the sum of the
areas of all of the sides.
There are six sides—each side has an area of 4.
The surface area is 6 • 4 = 24 square units.
The volume of this solid is 4 • 2 • 1 = 8 cubic units.
The surface area of this solid is the sum of the
areas of all of the sides:
Two sides have an area of 2 • 4 = 8.
Two sides have an area of 1 • 4 = 4.
Two sides have an area of 1 • 2 = 2.
Therefore, the surface area is
2(8 + 4 + 2) = 28 square units.
4
4
Solve each problem.
2
1) What is the volume of this cube? _____________________
What is its surface area? _____________________
4
8
2) What is the volume of this rectangular prism? _____________________
What is its surface area? _____________________
3) What is the volume of this rectangular prism? _____________________
2
What is its surface area? _____________________
4) What is the volume of a 1 x 64 x 1 prism? _____________________
What is the surface area of such a prism? _____________________
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16
2
Pre-Algebra
Name
Date
Period
Chapter 9
Community
Connection
School Measures Up
9
The following formulas are useful in determining the perimeter or area of
a rectangle or the volume of a rectangular prism.
Area
A = lw
Perimeter
P = 2l + 2w
Volume
V = lwh
Use a tape measure and the formulas above to help find the following.
1) The perimeter of your classroom
l ____________
w ____________
P ____________
w ____________
A ____________
2) The area of your classroom
l ____________
3) The perimeter of your school’s basketball court
l ____________
w ____________
P ____________
4) The area of your school’s basketball court
l ____________
w ____________
A ____________
5) The volume of a single Pre-Algebra book
l ____________
w ____________
h ____________
V ____________
h ____________
V ____________
6) The volume of your school locker
l ____________
w ____________
7) The volume of a box of cereal such as cornflakes
l ____________
w ____________
h ____________
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V ____________
Pre-Algebra
SELF-STUDY GUIDE
Name ooooooooooooooooooooooooooooooooooooo
CHAPTER 9: Equations from Geometry
Goal 9.1
To find the perimeters of regular and irregular polygons
Date
Assignment
Score
_________ 1: Read pages 238–240. Complete Exercises A–C on pages 240–241.
_________
_________ 2: Complete Workbook Activity 79.
_________
_________ 3: Read pages 242–243. Complete Exercises A–C on pages 244–245.
_________
_________ 4: Complete Workbook Activity 80.
_________
_________ 5: Read pages 246–247. Complete Exercises A–B on pages 248–249.
_________
_________ 6: Complete Workbook Activity 81.
_________
Comments:
Goal 9.2
To calculate the areas of regular and irregular polygons
Date
Assignment
Score
_________ 7: Read pages 250–251. Complete Exercises A, B, D on pages 251–253.
_________
_________ 8: Read and complete the Calculator Practice on pages 252–253.
_________
_________ 9: Complete Workbook Activity 82.
_________
_________ 10: Read pages 254–255. Complete Exercises A–C on page 255.
_________
_________ 11: Complete Workbook Activity 83.
_________
_________ 12: Read pages 256–257. Complete Exercises A–B on page 257.
_________
_________ 13: Complete Workbook Activity 84.
_________
_________ 14: Read page 258. Complete Exercise A on page 259.
_________
_________ 15: Complete Workbook Activities 85 and 86.
_________
Comments:
©AGS® American Guidance Service, Inc. Permission is granted to reproduce for classroom use only.
Pre-Algebra
SELF-STUDY GUIDE
Name ooooooooooooooooooooooooooooooooooooo
CHAPTER 9: Equations from Geometry, continued
Goal 9.3
To use formulas to find the volumes of cubes, rectangular prisms, and square pyramids
Date
Assignment
Score
_________ 16: Read pages 260–262. Complete Exercises A, C on pages 262–263.
_________
_________ 17: Read and complete the Calculator Practice on page 263.
_________
_________ 18: Complete Workbook Activity 87.
_________
Comments:
Goal 9.4
To determine the circumferences and areas of circles
Date
Assignment
Score
_________ 19: Read pages 264–266. Complete Exercises A–B on pages 266–267.
_________
_________ 20: Read and complete the Calculator Practice on page 267.
_________
_________ 21: Complete Workbook Activity 88.
_________
Comments:
Goal 9.5
To use formulas to find the volumes of cylinders and spheres
Date
Assignment
Score
_________ 22: Read page 268. Complete Exercises A–C on pages 269.
_________
_________ 23: Complete Workbook Activity 89.
_________
_________ 24: Read and complete the Application Exercise on page 270.
_________
_________ 25: Complete the Chapter 9 Review on pages 271–273.
_________
Comments:
Student’s Signature ____________________________________ Date _____________________
Instructor’s Signature __________________________________ Date _____________________
©AGS® American Guidance Service, Inc. Permission is granted to reproduce for classroom use only.
Pre-Algebra
Name
Date
Chapter 9
Period
Activity
Perimeters of Polygons
75
Directions Find the perimeter of each figure.
6.338 mm
1)
2)
20 ft
_________
15 ft
3)
6.338 mm
4)
3
5}4}
3
5}4}
in.
3.875 mm
3.875 mm
10 ft
in.
3
5}4} in.
_________
9.6 m
9.6 m
9.6 m
_________
_________
9.6 m
Directions Solve each problem to find the perimeter.
2
5) What is the perimeter of a rhombus with each side measuring 1}3}
yards?
___________________
6) The sides of a quadrilateral measure 11.68 m, 5.73 m, 4.66 m, and
12.99 m. What is the perimeter?
___________________
2
1
7) A scalene triangle has sides measuring 3}3} cm, 4}3} cm, and 6 cm. What
is the perimeter?
___________________
8) What is the perimeter of an equilateral triangle with each side
measuring 91.4 ft?
___________________
Directions Solve each problem.
9) Shona is working during the summer painting lines on basketball
courts. Each pint of paint will cover a perimeter of 63 feet. The
perimeter of the Kohl Center’s basketball court is 132.3 feet.
How many pints of paint will Shona use?
___________________
10) Beth’s garden is in the shape of a rectangle. It has a total perimeter of
35 feet. The lengths of two sides are 10.8 feet each. What are the lengths
of the other two sides?
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___________________
Pre-Algebra
Name
Date
Period
Workbook
Activity
Perimeters of Polygons
EXAMPLE
Chapter 9
79
6 cm
5 cm
Find the perimeter of this figure.
Perimeter = 5 + 6 + 8 = 19 cm
8 cm
Directions Find the perimeter of each figure.
3 mm
1)
3 mm
2)
3 mm
1
2}2}
3 yd
_________
4)
1
2}2}
yd
9.44 ft
6.2 ft
_________
3 mm
3)
4.7 ft
9.22 in.
11.93 in.
yd
3 yd
_________
7.25 in.
_________
Directions Solve each problem to find the perimeter.
7
1
1
1
5) The sides of a quadrilateral measure 6}8} ft, 4}2} ft, 3}8} ft, and 7}2} ft. What is
the perimeter?
__________________
6) Two sides of an isosceles triangle measure 6.42 m each. The remaining
side measures 9.73 m. What is the perimeter of the triangle?
__________________
7) Each side of an equilateral triangle measures 48 yards. What is the
perimeter?
__________________
8) A scalene triangle has sides measuring 532.6 ft, 429.3 ft, and 830.6 ft.
What is the perimeter?
__________________
Directions Solve each problem.
9) Hector made a dog kennel in his backyard. He used a total of 28 feet of
fencing, including the gate. If two sides of the kennel are ten feet each,
what are the lengths of the other two sides?
__________________
10) Maya has 13.75 inches of gold string, which she wants to glue around
a picture frame in the shape of an equilateral triangle. Each side of the
triangle is 4.25 inches. Does she have enough string?
©AGS® American Guidance Service, Inc. Permission is granted to reproduce for classroom use only.
__________________
Pre-Algebra
Name
Date
Period
Chapter 9
Activity
Perimeters of Regular Polygons
76
Directions Find the perimeter of each regular polygon.
1)
2)
1
1}2} in.
4 mm
___________
___________
3)
4)
75 ft
5.62 m
___________
___________
5)
6)
3
2}4}
4.93 mi
yd
___________
___________
Directions Find the number of sides that each shape has.
7) Each side of a regular polygon measures 5.3 ft. The perimeter of the
polygon is 74.2 ft. How many sides does this polygon have?
8) The perimeter of a regular polygon is
measures
5
1}8}
1
34}8}
__________________
m. Each side of the polygon
m. How many sides does this polygon have?
__________________
9) The sum of all sides of a regular polygon is 144 cm. Each side measures
16 cm. How many sides does this polygon have?
__________________
10) The perimeter of a regular polygon is 117.26 inches. Each side
measures 9.02 inches. How many sides does this polygon have?
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__________________
Pre-Algebra
Name
Date
Chapter 9
Period
Workbook
Activity
Perimeters of Regular Polygons
80
EXAMPLE
Each side of a regular pentagon measures
6.9 cm. Find the perimeter.
6.9 cm
P = 5(6.9) = 34.5 cm
Directions Find the perimeter of each regular polygon.
1)
2)
8 ft
3)
5
2}8} in.
_________
4)
1.062 mm
200 dm
_________
_________
5)
1
32}3} yd
_________
6)
_________
7.18 mi
_________
Directions Find the number of sides that each shape has.
7) Each side of a regular polygon measures 3.67 m. The perimeter of the
polygon is 47.71 m. How many sides does this regular polygon have?
_____________________
8) The perimeter of a regular polygon is 1,071 cm. Each side of the
polygon measures 63 cm. How many sides does this regular polygon
have?
_____________________
9) The sum of all sides of a regular polygon is 253 ft. Each side measures
11 ft. How many sides does this regular polygon have?
_____________________
10) The perimeter of a regular polygon is 13.125 ft. Each side measures
1.875 ft. How many sides does this regular polygon have?
_____________________
©AGS® American Guidance Service, Inc. Permission is granted to reproduce for classroom use only.
Pre-Algebra
Name
Date
Chapter 9
Period
Activity
Perimeters of Irregular Polygons
77
Directions Find the perimeter of each polygon.
1
1)
2)
10}4} in.
1
8}4}
in.
15.7 cm
5.9 cm
3
5}8} in.
13.8 cm
11.6 cm
7
1
8}8} in.
6}2} in.
___________
___________
17.7 m
3)
4)
18.32 ft
31 m
11 ft
55.3 m
10 ft
14 m
21.1 m
15 ft
11.45 ft
___________
7.63 ft
___________
45 m
15.6 in.
5)
16.4 in.
6)
2
6}3} km
18.7 in.
2 km
3
5}4}
11 in.
31.1 in.
km
6 km
___________
25 in.
___________
Directions Find the measure of each missing x.
1
1.8
6.2
7)
6.1
5.9
8}2}
8)
x
1
12}3}
8.5
4.5
x
5
_________
7.8
9) Triangle WBC is an equilateral triangle.
4
10) EGHI is a square.
B
x
W
x
C
425 m
21.2 ft
_________
_________
1
3}2}
E
85 ft
G
F
J
I
100 ft
x
_________
H
321 m
©AGS® American Guidance Service, Inc. Permission is granted to reproduce for classroom use only.
Pre-Algebra
Name
Date
Chapter 9
Period
Workbook
Activity
Perimeters of Irregular Polygons
81
9.2 in.
EXAMPLE
Find the perimeter of this polygon.
7.8 in.
6.2 in.
5.7 in.
P = 6.2 + 5.7 + 5.4 + 4.3 + 7.8 + 9.2 = 38.6 in.
5.4 in.
4.3 in.
Directions Find the perimeter of each polygon.
1
7
32 m
1)
58 m
2)
5
28
3
54 m
5.2 cm
4.6 ft
5.4 ft
2.8 ft
m
9 cm
23 mm
16 cm
m
_________
4)
8 cm
9.3 cm
6.7 ft
1
74
12.22 cm
3)
15 mm
_________
_________
2
5)
6)
93 yd
12.5 in.
13.6 in.
15.2 in.
19.5 mm
5 yd
3
84
58.5 mm
8 in.
yd
28 in.
9 yd
32 mm
22 in.
46.7 mm
_________
_________
_________
Directions Find the measure of each missing x. Then find the perimeter of each polygon.
1
7)
22
8)
17
2
2
10
3
14
9)
A
28
x
14
_________
3
24
_________
7 yd
C
yd
8
7 yd
_________
E
_________
ACEF is a square.
10)
x
_________
x
S
Q
D
9 yd
_________
R
B
x
F
2
1
3
x
1
18
31.4 m
_________
20.1 m
_________
Triangle QRS is an equilateral triangle.
©AGS® American Guidance Service, Inc. Permission is granted to reproduce for classroom use only.
Pre-Algebra
Name
Date
Period
Chapter 9
Activity
Areas of Rectangles and Squares
78
Directions Find the area of each rectangle.
1) Rectangle DEFG with l = 3 mm and w = 5 mm
_________________
2) Rectangle EDCF with l = 11 in. and w = 4 in.
_________________
3) Rectangle TGBY with l = 19.6 yd and w = 8 yd
_________________
4) Rectangle UJMI with l = 12 m and w = 4.75 m
_________________
5) Rectangle
6) Rectangle
1
1
WSED with l = 6}3} mi and w = 8}2} mi
1
1
LKJH with l = 9}4} yd and w = 5}5} yd
_________________
_________________
Directions Find the area of each square.
7) Square PLMK with s = 7 dm
_________________
8) Square GHIJ with s = 25 in.
_________________
9) Square BNVC with s = 6.1 m
_________________
10) Square XMSH with s = 64.6 mm
11) Square
12) Square
1
WXYZ with s = 9}5} ft
2
QYAH with s = 5}3} yd
_________________
_________________
_________________
Directions Use the formula A = s2 and a calculator to find the area of each square.
13) s = 30 m
__________________
16) s = 84 yd
__________________
14) s = 32.4 km
__________________
17) s = 3.67 mi
__________________
15) s = 7.9 ft
__________________
18) s = 29.08 km
__________________
Directions Solve each problem
19) Charlie is planting new grass in part of his backyard. The dimensions
of the area to be seeded are 30 ft long and 15 ft wide. Each box of grass
seed will cover 100 ft2. How many boxes of seed will Charlie use?
______________________
20) Every spring Darla rototills her garden. The rectangular garden
measures 43.5 feet by 25.8 feet. What is the area of the garden?
What is the perimeter?
______________________
©AGS® American Guidance Service, Inc. Permission is granted to reproduce for classroom use only.
Pre-Algebra
Name
Date
Chapter 9
Period
Workbook
Activity
Areas of Rectangles and Squares
EXAMPLE
82
L
M
Find the area of square LMNO.
Substitute 5.2 into the formula A = s2.
A = (5.2)2 = 27.04 in.2
O
N
5.2 in.
Directions Find the area of each rectangle.
1) Rectangle DKJF with l = 8 ft and w = 6 ft
________________
2) Rectangle AOPU with l = 13 m and w = 4 m
________________
3) Rectangle QWER with l = 15.5 cm and w = 8 cm
________________
4) Rectangle BNMA with l =
1
4}2}
yd and w =
1
6}4}
yd
________________
Directions Find the area of each square.
5) Square ABCD with s = 10 mm
6) Square JKLM with s = 21 ft
__________
__________
7) Square YTRE with s = 4.2 cm
8) Square PLKM with s =
1
5}2}
m
__________
__________
Directions Use the formula A = s2 and a calculator to find the area of each square.
9) s = 23 m
__________
11) s = 8.5 cm
__________
10) s = 6.7 ft
__________
12) s = 42 in.
__________
13) s = 1.42 mi __________
Directions Solve each problem.
14) Allen is painting a family room. Two walls are 8 ft high and 15 ft long.
The other two walls are 8 ft high and 9 ft long. Allen has one gallon of paint,
which will cover 400 ft2 of walls. Will he have enough paint? Explain.
__________________________________________________________________________
15) Consuela cuts lawns as a part-time job. The last lawn she cut was rectangular and totaled
1,365 yd2. One side of the lawn was 35 yards long. What was the length of the other side?
_________________
©AGS® American Guidance Service, Inc. Permission is granted to reproduce for classroom use only.
Pre-Algebra
Name
Date
Chapter 9
Period
Activity
Areas of Triangles
79
Directions Find the area of each figure.
1)
2)
3)
11 ft
13 m
12 in.
_________
10 in.
4)
23 ft
24 m
_________
5)
_________
6)
4 cm
6 km
30 yd
9 cm
7 km
_________
_________
_________
14 yd
Directions Find the base or height of each triangle.
7) The area of a triangle is 40 m2 and the height is 10 m. What is the base?
________________
8) The area of a triangle is 30 in.2 and the base is 10 in. What is the height?
________________
9) The area of a triangle is 45 yd2 and the base is 9 yd. What is the height?
________________
10) The area of a triangle is 72 km2 and the height is 6 km. What is the base?
________________
11) The area of a triangle is 6 mm2 and the height is 4 mm. What is the base?
________________
12) The area of a triangle is 20 mi.2 and the base is 5 mi. What is the height?
________________
13) The area of a triangle is 12 ft2 and the base is 3 ft. What is the height?
________________
14) The area of a triangle is 100 in.2 and the height is 10 in. What is the base?
________________
15) The area of a triangle is 120 cm2 and the height is 8 cm. What is the base?
________________
16) The area of a triangle is 24.5 mm2 and the base is 7 mm. What is the height?
________________
17) The area of a triangle is 13.5 yd2 and the height is 9 yd. What is the base?
________________
18) The area of a triangle is 165 ft2 and the base is 30 ft. What is the height?
________________
Directions Solve each problem.
19) Ava is making stage decorations for a school play. She must decorate a
triangle with an area of 45 ft2. The base is 9 ft. What is the height?
________________
20) William’s rectangular flower garden is 25 ft by 16 ft. It is divided into
two triangles—one triangle of pink flowers and the other of orange
flowers. William says one triangle is 190 ft2 and the other is 210 ft2.
Is he correct?
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________________
Pre-Algebra
Name
Date
Period
Workbook
Activity
Areas of Triangles
EXAMPLE
Chapter 9
83
Y
Find the area of triangle XYZ.
1
Use the formula A = }2}bh.
1
A = }2}(6)(10)
1
A = }2}(60)
A = 30
10 m
m2
X
6m
Z
Directions Find the area of each figure.
1)
2)
6 ft
3)
15 m
16 km
4 ft
_________
12 m
_________
9 km
_________
Directions Find the base or height of each triangle.
4) The area of a triangle is 12 ft2 and the base is 4 ft. What is the height?
______________
5) The area of a triangle is 32 in2 and the height is 8 in. What is the base?
______________
6) The area of a triangle is 15 m2 and the base is 10 m. What is the height?
______________
7) The area of a triangle is 36 yd2 and the height is 9 yd. What is the base?
______________
8) The area of a triangle is 36 km2 and the height is 12 km. What is the base?
______________
Directions Solve these problems.
9) Howard is constructing a triangular garden edge out of brick. The
base of the garden is 15 ft. The area is 165 ft2. What is the height of the
triangle?
____________
10) Jana is making curtains in the shape of triangles. She needs to make
two triangle curtains for one window. The triangles have a base of 2 ft
and a height of 4 ft. What is the total area of the triangle curtains for
one window?
____________
©AGS® American Guidance Service, Inc. Permission is granted to reproduce for classroom use only.
Pre-Algebra
Name
Date
Chapter 9
Period
Activity
Areas of Trapezoids and Parallelograms
80
Directions Find the area of each quadrilateral.
1)
2)
5 ft
3)
7 ft
9 yd
_________
4)
30 m
10 yd
4 ft
15 in.
_________
15 m
_________
5)
8.73 m
20 in.
3.65 m
19 in.
_________
_________
Directions Find the base or height of each quadrilateral.
6) The bases of a trapezoid equal 13 cm and its area is 65 cm2. What is its height? _____________
7) A parallelogram has a height of 12 m and an area of 204 m2.
What is the length of its base? _____________
8) The bases of a trapezoid equal 26 ft and its area is 195 ft2. What is its height? _____________
9) A trapezoid has one base 7 yd long and another base 11 yd long. Its area is 144 yd2.
What is its height? _____________
10) A parallelogram has a height of 28 mm and an area of 476 mm2.
What is the length of its base? _____________
11) The bases of a trapezoid equal 108 cm and its area is 1,566 cm2. What is its height? _____________
12) A trapezoid has one base 6.8 mi long and another base 9.7 mi long. Its area is 127.875 mi2.
What is its height? _____________
13) The bases of a trapezoid equal 32 cm and its area is 64 cm2. What is its height? _____________
14) A parallelogram has a height of 23 ft and an area of 966 ft2. What is the length
of its base? _____________
15) With a base of 104 m and an area of 22,776 m2, what is the height
of the parallelogram? _____________
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Pre-Algebra
Name
Date
Period
Workbook
Activity
Areas of Trapezoids and Parallelograms
EXAMPLE
Find the area of trapezoid STRU.
A=
b1 + b2
}
2 h
A=
6 + 20
}}(10)
2
6m
T
Chapter 9
84
R
10 m
=
26
}}(10)
2
S
A = (13)(10) = 130 m2
U
20 m
Directions Find the area of each quadrilateral.
1)
2)
4 in.
3)
24 ft
6m
5 in.
8 in.
9m
_________
_________
13 ft
_________
Directions Find the base or height of each quadrilateral.
4) A parallelogram has a height of 9 cm and an area of 108 cm2.
What is the length of its base? ____________
5) A trapezoid has one base 6 ft long and another base 8 ft long. Its area is 240 ft2.
What is its height? ____________
6) If a parallelogram has a base of 11 m and an area of 176 m2, what is its height?
____________
7) A parallelogram has a height of 12 in. and an area of 168 in.2.
What is the length of its base? ____________
8) The bases of a trapezoid equal 16 km and its area is 32 km2. What is its height? ____________
9) If a parallelogram has a base of 13 mm and an area of 78 mm2,
what is its height? ____________
10) The bases of a trapezoid equal 17 yd and its area is 68 yd2. What is its height? ____________
©AGS® American Guidance Service, Inc. Permission is granted to reproduce for classroom use only.
Pre-Algebra
Name
Date
Chapter 9
Period
Activity
Areas of Irregular Polygons
81
Directions Find the area of each polygon.
6
1)
2)
3
10
10
4
4
6
5
2
5
5
10
9
__________
__________
8
3)
4)
4
4
12
8
8
4
5
7
4
__________
5)
6)
12
__________
7
7
5
10
11
14
13
11
__________
16
7)
__________
22
8)
7
7
20
36
15
23
20
20
13
__________
17
9)
7
10)
30
4
5 6
3
__________
23
20
25
35
35
2
__________
25
__________
21
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Pre-Algebra
Name
Date
Chapter 9
Period
Workbook
Activity
Areas of Irregular Polygons
EXAMPLE
85
Find the area of this polygon.
3
Divide the polygon into smaller regions to calculate the areas.
7
A = (5 • 7) + (2 • 3)
2
A = 35 + 6 = 41 units2
5
Directions Find the area of each polygon.
6
1)
3
2)
2
3
1
2
2
7
10
7
_________
_________
1
10
3)
4)
10
5
8
4
8
6
5
6
7
3
_________
_________
3
5
5)
6
7
10
10
3
3
14
_________
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Pre-Algebra
Name
Date
Chapter 9
Period
Workbook
Activity
Working with Areas of Shapes
86
Directions Find the area of each rectangle or square.
1) Rectangle POUI with l = 9 in. and w = 3.85 in.
2) Rectangle AEYR with l =
1
3}3}
mi and w =
3) Square YHNJ with s = 16.3 yd
1
1
7}2}
mi
________________
________________
________________
4) Square QAZW with s = 3}4} ft
________________
5) Square LMNO with s = 12.33 mi
________________
Directions Use the area to find the base or height of each triangle,
trapezoid, or parallelogram.
6) The area of a triangle is 14 ft2 and the base is 7 ft. What is the height?
________________
7) The area of a triangle is 15 mm2 and the height is 5 mm. What is the base?
________________
8) The area of a triangle is 9 cm2 and the base is 3 cm. What is the height?
________________
9) The area of a triangle is 50 in.2 and the base is 10 in. What is the height?
________________
10) The area of a triangle is 80 m2 and the height is 8 m. What is the base?
________________
11) The area of a triangle is 40.5 ft2 and the base is 9 ft. What is the height?
________________
12) The area of a triangle is 17.5 dm2 and the height is 7 dm. What is the base?
________________
13) A trapezoid has one base 23 in. long and another base 27 in. long. Its area is 400 in2.
What is its height? ________________
14) The bases of a trapezoid equal 68 mm and its area is 1,768 mm2.
What is its height? ________________
15) A parallelogram has a height of 23 mi and an area of 667 mi2.
What is the length of its base? ________________
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Pre-Algebra
Name
Date
Chapter 9
Period
Activity
Volume
82
Directions Find the volume of each figure.
1)
4m
2)
3)
2 ft
7 cm
3 cm
5 ft
4m
3 ft
4m
_________
4)
5)
10 in.
3 cm
_________
2 yd
_________
6)
8 mm
10 in.
4 mm
9 yd
10 in.
_________
6 yd
4 mm
_________
_________
Directions Use the formula V = e3 and a calculator to find the volume of
each cube.
7) e = 32 mi
_______________
13) e = 67 in.
_______________
8) e = 1.7 in.
_______________
14) e = 33 m
_______________
9) e = 116 km
_______________
15) e = 17.2 mm
_______________
10) e = 0.4 mm
_______________
16) e = 112 ft
_______________
11) e = 30 cm
_______________
17) e = 0.95 dm
_______________
12) e = 1.2 ft
_______________
18) e = 250 m
_______________
Directions Solve each problem.
19) Jack received a package full of books from his brother in California.
The package was 20 inches by 20 inches and 10 inches deep. Each
book was 10 inches by 5 inches and 4 inches thick. How many books
were in the package?
__________________
20) Liz’s pool is 20 feet by 13 feet and 5 feet deep. What is the volume of
her pool?
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__________________
Pre-Algebra
Name
Date
Chapter 9
Period
Workbook
Activity
Volume
EXAMPLE
87
Find the volume of this rectangular prism.
4
V = lwh
7
V = (7)(5)(4) =140 in.3
5
Directions Find the volume of each figure.
1)
2)
3)
6 cm
3 ft
6m
6 ft
6 cm
6 cm
2m
4 ft
_________
_________
2m
_________
Directions Use the formula V = e3 and a calculator to find the volume of each cube.
4) e = 23 mm
____________
10) e = 68 dm
____________
5) e = 1.8 in.
____________
11) e = 43 m
____________
6) e = 126 ft
____________
12) e = 19.2 in.
____________
7) e = 0.9 mi
____________
13) e = 202 ft
____________
8) e = 50 cm
____________
9) e = 1.02 km
____________
Directions Solve each problem.
14) Marcus is shipping books to his brother in New York. The box is 10
inches by 10 inches and 6 inches deep. Each book is 5 inches by 5
inches and 2 inches thick. How many books can Marcus ship in
one package?
____________
15) Lisa’s suitcase is 18 inches wide, 32 inches high, and 36 inches long.
What is the volume of the suitcase?
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____________
Pre-Algebra
Name
Date
Period
Chapter 9
Activity
Circumferences and Areas of Circles
83
Directions Find the circumference of a circle with the given radius or
diameter. Use the formula C = ¹d. Use 3.14 for ¹.
1) radius = 2 km
_______________
6) radius = 4 yd
_______________
2) diameter = 8 ft
_______________
7) diameter = 14 in.
_______________
3) radius = 3 cm
_______________
8) diameter = 16 m
_______________
4) diameter = 7 mm
_______________
9) radius = 9 ft
_______________
5) radius = 5 in.
_______________
10) diameter = 20 m
_______________
Directions Find the area of a circle with the given radius or diameter.
Use 3.14 for ¹.
11) radius = 4 ft
_______________
16) radius = 5 m
_______________
12) diameter = 12 cm
_______________
17) radius = 7 mi
_______________
13) radius = 8 yd
_______________
18) diameter = 16 ft
_______________
14) diameter = 6 km
_______________
19) radius = 12 in.
_______________
15) diameter = 10 in.
_______________
20) radius = 1 m
_______________
Directions Use a calculator and the formula A = ¹r2 to find the areas of
circles with the following measures. Use 3.14 for ¹.
21) diameter = 4.5 mi
_______________
26) diameter = 84 km
_______________
22) radius = 222 yd
_______________
27) radius = 13.5 yd
_______________
23) radius = 5.6 m
_______________
28) diameter = 0.75 mm
_______________
24) diameter = 7.5 ft
_______________
29) radius = 605 cm
_______________
25) radius = 1.6 in.
_______________
30) diameter = 994 ft
_______________
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Pre-Algebra
Name
Date
Period
Workbook
Activity
Circumferences and Areas of Circles
EXAMPLE
Chapter 9
88
Find the circumference and area of a circle with a radius of 5 feet.
To find the circumference, use the formula C = ¹d.
First, calculate the diameter.
2 • 5 = 10 feet
C = (3.14)(10) = 31.4 feet
To find the area, use the formula A = ¹r2.
A = (3.14)(52) = 78.5 feet2
Directions Find the circumference of a circle with the given radius or
diameter. Use the formula C = ¹d. Use 3.14 for ¹.
1) radius = 4 in.
_________________
4) diameter = 10 mm
_________________
2) diameter = 6 ft
_________________
5) radius = 7 km
_________________
3) radius = 2 m
_________________
Directions Find the area of a circle with the given radius or diameter.
Use the formula A = ¹r2. Use 3.14 for ¹.
6) radius = 3 yd
_________________
11) radius = 6 km
_________________
7) diameter = 10 cm
_________________
12) radius = 5 mi
_________________
8) radius = 7 ft
_________________
13) diameter = 6 in.
_________________
9) diameter = 4 m
_________________
14) radius = 8 ft
_________________
10) diameter = 14 in.
_________________
15) radius = 10 m
_________________
Directions Use a calculator and the formula A = ¹r2 to find the areas of
circles with the following measures. Use 3.14 for ¹.
16) diameter = 1.25 yd
_________________
19) diameter = 9.5 m
_________________
17) radius = 215 mi
_________________
20) radius = 1.8 km
_________________
18) radius = 6.7 ft
_________________
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Pre-Algebra
Name
Date
Period
Chapter 9
Activity
Volumes of Cylinders and Spheres
84
Directions Find the volume of a cylinder with the given height and
radius or diameter. Use the formula V = ¹r2h. Use 3.14 for ¹.
1) diameter = 3 mm; height = 6 mm
_______________
2) radius = 3 ft; height = 8 ft
_______________
3) diameter = 9 in.; height = 7 in.
_______________
4) radius = 2 yd; height = 1 yd
_______________
5) diameter = 1 cm; height = 5 cm
_______________
6) diameter = 5 m; height = 6 m
_______________
7) radius = 8 cm; height = 14 cm
_______________
8) radius = 1 ft; height = 7 ft
_______________
9) radius = 8 yd; height = 15 yd
_______________
10) diameter = 70 cm; height = 60 cm
_______________
Directions Find the volume of a sphere with the given radius or
4
diameter. Use the formula V = }3}¹r3. Use 3.14 for ¹.
11) radius = 12 mm
_______________
15) diameter = 60 ft
_______________
12) radius = 6 ft
_______________
16) radius = 15 cm
_______________
13) diameter = 33 cm
_______________
17) diameter = 21 in.
_______________
14) radius = 90 yd
_______________
18) diameter = 6 m
_______________
Directions Solve each problem.
19) Which has the greater volume, a cylinder with a diameter of 4 cm
and a height of 4 cm or a sphere with a diameter of 4 cm? Explain. _________________________
_______________________________________________________________________________
20) Ali told Jenny that the volume of a cylinder is always larger than the volume
of a sphere with the same radius. Explain why this is a false statement. ______________________
_______________________________________________________________________________
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Pre-Algebra
Name
Date
Chapter 9
Period
Workbook
Activity
Volumes of Cylinders and Spheres
EXAMPLE
89
Find the volume of this cylinder.
Use the formula V = πr2h.
10 in.
V = (3.14)(6)2(10)
V = (3.14)(36)(10)
6 in.
V = 1,130.4 in.3
Directions Find the volume of a cylinder with the given height and
radius or diameter. Use the formula V = πr2h. Use 3.14 for π.
1) diameter = 6 in; height = 5 in.
________
6) diameter = 4 cm; height = 4 cm
________
2) radius = 4 ft; height = 7 ft
________
7) radius = 9 m; height = 13 m
________
3) diameter = 10 mm; height = 8 mm ________
8) radius = 1 ft; height = 6 ft
________
4) radius = 3 cm; height = 2 cm
________
9) radius = 7 cm; height = 14 cm
________
5) diameter = 2 yd; height = 6 yd
________
10) diameter = 6 yd; height = 50 yd
________
Directions Find the volume of a sphere with the given radius or
4
diameter. Use the formula V = 3πr3. Use 3.14 for π.
11) radius = 3 cm
________
15) diameter = 30 cm
________
12) radius = 6 ft
________
16) radius = 12 ft
________
13) diameter = 48 mm
________
17) diameter = 21 m
________
14) radius = 9 yd
________
18) diameter = 15 in.
________
Directions Solve each problem.
19) George filled a plastic bag with water until it had a diameter of 9 inches.
What was the volume of the bag?
____________
20) Lin has two boxes to choose from to mail a package to her sister in Florida.
One is a rectangular box measuring 12 inches long, 9 inches high, and
10 inches wide. The other is a cylinder with a diameter of 10 inches and a height
of 14 inches. She wants the larger box. Which one should she pick? Explain.
____________________________________________________________________________
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Pre-Algebra
Name
Date
Chapter 9
Period
Mastery
Test
page 1
Chapter 9 Mastery Test
Directions Find the perimeter or circumference of each figure.
1)
2)
3 in.
3)
9 cm
9 cm
15 cm
4 in.
_________
4)
_________
5)
12.5 ft
_________
6)
2m
5 ft
5 ft
4.3 m
8.375 in.
22.5 ft
_________
_________
_________
Directions Find the volume of each figure. When necessary, round your
answer to the nearest tenth.
7)
8)
30 cm
6 mm
9 cm
_________
9)
9 cm
_________
10)
40 in.
8 in.
_________
_________
15 in.
©AGS® American Guidance Service, Inc. Permission is granted to reproduce for classroom use only.
Pre-Algebra
Name
Date
Chapter 9
Period
Mastery
Test
page 2
Chapter 9 Mastery Test, continued
Directions Find the area of each figure.
11)
12)
13)
9 ft
9.4 m
3.1 m
21.5 ft
_________
14)
5.2 m
_________
15)
21 mm
_________
16)
15.68 m
18 in.
17.45 m
15 mm
30 mm
_________
17)
_________
_________
7.7 m
18)
6 yd
29.7 cm
_________
_________
19.8 cm
Directions Find the perimeter and the area of each figure.
19)
20)
2
2
5
3
4
6
1
4
_________
2
4
_________
5
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Pre-Algebra
Name
Date
Period
Chapter 9
Cumulative
Mastery Test
page 1
Chapter 9 Cumulative Mastery Test
Directions Estimate each sum, difference, product, or quotient.
1) 41 • 79
____________
3) 589 – 197
____________
2) 81,068 + 10,105
____________
4) 1,177 ÷ 59
____________
Directions Write each decimal as a fraction in simplest form.
5) 0.72
____________
6) 0.008
____________
Directions Write each fraction as a terminating or repeating decimal.
11
7) }20}
____________
1
8) }6}
____________
Directions Factor or simplify each expression.
9) 4(a + b)
____________
11) 3x + 12y
____________
10) 20m – 5n
____________
12) 10(g – 6h)
____________
Directions Label each fraction proper or improper.
3
13) }25}
____________
0
15) }4}
____________
2
14) }2}
____________
19
16) }1}3
____________
Directions Express each improper fraction as a whole or mixed number
in simplest form.
18
17) }8}
____________
42
19) }7}
____________
15
18) }11}
____________
3
20) }2}
____________
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Pre-Algebra
Name
Date
Chapter 9
Period
Cumulative
Mastery Test
page 2
Chapter 9 Cumulative Mastery Test, continued
Directions Express each mixed number as an improper fraction.
3
21) 2}4}
7
22) 5}1}2
____________
____________
Directions Simplify each expression using the order of operations.
23) 2(5 – 3) – 4
____________
26) (16 – 7) ÷ 3
____________
24) 28 + 12 ÷ 2
____________
27) 8(12 – 9) + 2 • 2
____________
25) 10 + 5(5)
____________
28) 50 – 15 • 2 + 6 ÷ 3
____________
Directions Solve for the variable in each proportion.
3
w
29) }4} = }24}
____________
1
2
31) }8} = }h}
____________
c
5
30) }18} = }6}
____________
6
24
32) }m} = }4}
____________
Directions Compare each pair. Use <, >, or =.
33) –2 Â 1
____________
34) |4| Â –5
____________
Directions Find the value of each expression.
35) 33
____________
37) (–2)5
____________
36) 102
____________
38) (–1)4
____________
Directions Find the perimeter and area of each figure.
39)
40)
10 in.
6.4 cm
______________
12 in.
______________
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______________
______________
Pre-Algebra