Premier university in CALABARZON offering academic programs

A premier university in CALABARZON, offering
academic programs and related services designed to
respond to the requirements of the Philippines and the
global economy, particularly Asian Countries.

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The University shall primarily provide advanced
education, professional, technological and vocational
instruction in agriculture, fisheries, forestry, science,
engineering, industrial technologies, teacher
education, medicine, law, arts and sciences,
information technologies and other related fields. It
shall also undertake research and extension services
and provide progressive leadership in its areas of
specialization.

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In pursuit of the college vision/mission the
College of Education is committed to develop the full
potentials of the individuals and equip them with
knowledge, skills and attitudes in Teacher Education
allied fields to effectively respond to the increasing
demands, challenges and opportunities of changing
time for global competitiveness.

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Produce graduate who can demonstrate and practice
the professional and ethical requirement for the
Bachelor of Secondary Education such as:

1. To serve as positive and powerful role models in
pursuit of learning thereby maintaining high regards to
professional growth.
2. Focus on the significance of providing wholesome and
desirable learning environment.
3. Facilitate learning process in diverse type of learners.
4. Use varied learning approaches and activities,
instructional materials and learning resources.
5. Use assessment data plan and revise teaching –
learning plans.
6. Direct and strengthen the links between school and
community activities.
7. Conduct research and development in Teacher
Education and other related activities.
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This Teacher‟s “Module in solving Polynomials” is part of the requirements in
Educational Technology 2 under the revised curriculum for Bachelor in Elementary
Education based on CHED Memorandum Order (CMO)-30, Series of 2004. Educational
Technology 2 is a three (3)-unit course designed to introduce both traditional and innovative
technologies to facilitate and foster meaningful and effective learning where students are
expected to demonstrate a sound understanding of the nature, application and production of
the various types of educational technologies.
The students are provided with guidance and assistance of selected faculty
members of the College on the selection, production and utilization of appropriate
technology tools in developing technology-based teacher support materials. Through the
role and functions of computers especially the Internet, the student researchers and the
advisers are able to design and develop various types of alternative delivery systems.
These kinds of activities offer a remarkable learning experience for the education students
as future mentors especially in the preparation and utilization of instructional materials.
The output of the group‟s effort on this enterprises may serve as a contribution
to the existing body instructional materials that the institution may utilize in order to
provide effective and quality education. The lessons and evaluations presented in this
module may also function as a supplementary reference for secondary teachers and
students.
REVELLAME, JEZREEL A.
Workbook Developer
MAGAYON, LOUIE M.
Workbook Developer

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This Teacher‟s “Module in solving Polynomials” is part of the requirements in
Educational Technology 2 under the revised curriculum for Bachelor in Elementary Education
based on CHED Memorandum Order (CMO)-30, Series of 2004. Educational Technology 2 is a
three (3)-unit course designed to introduce both traditional and innovative technologies to
facilitate and foster meaningful and effective learning where students are expected to
demonstrate a sound understanding of the nature, application and production of the various
types of educational technologies.
The students are provided with guidance and assistance of selected faculty members
of the College on the selection, production and utilization of appropriate technology tools in
developing technology-based teacher support materials. Through the role and functions of
computers especially the Internet, the student researchers and the advisers are able to design
and develop various types of alternative delivery systems. These kinds of activities offer a
remarkable learning experience for the education students as future mentors especially in the
preparation and utilization of instructional materials.
The output of the group‟s effort on this enterprise may serve as a contribution to the
existing body instructional materials that the institution may utilize in order to provide effective
and quality education. The lessons and evaluations presented in this module may also function
as a supplementary reference for secondary teachers and students.

FOR-IAN V. SANDOVAL
Computer Instructor/Adviser
Educational Technology 2
DELIA F. MERCADO
Workbook Consultant
ARLENE G. ADVENTO
Workbook Consultant
LYDIA R. CHAVEZ
Dean College of Education

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The authors wish to express their sincerest gratitude and
appreciation to the support of those who assisted them to this requirement
for their time and effort to finish their workbook. Without their cooperation,
all of these have not been possible.
First, the authors want to express their deepest gratitude to our
Lord Jesus Christ, who serves as the greatest inspiration, for all the strength
and wisdom that He had gave to enhance their spiritual parts for carrying in
times of trouble for still giving hope.
Mr. For – Ian V. Sandoval, who spent his time in giving instruction
and sharing his knowledge in the production of this activity workbook.
Prof. Lydia R. Chavez, Dean of College of Education, for her
generous assistance.
Mrs. Arlene G. Advento and Mrs. Delia F. Mercado, consultants and
major teachers, for their valuable comments, suggestions, ideas and for
sharing their knowledge which made this workbook of more substance and
more meaningful.
Parents for their love, moral and financial supports in making this
workbook.
Classmates and friends, whose served as an inspiration and shared
their ideas on this workbook.
Someone special for support, love and inspiration.

The Authors

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Polygons are very useful graphical tool. Three- - dimensional shapes solids can easily be approximated
with few polygons, and, when good shading and texturing are applied, they can look reasonably realistic. They can be
drawn quickly and cover up very little storage space. Polygons are enclosed area bounded by at least three sides. A
polygon can be defined as a set of points or a set of line segments. The order in which the set of points are listed is
important. Different orders mean different polygons. These two polygons are made from the same set of points, listed in
a different order.
Space figures are figures whose points do not all lie in the same plane. In this unit, we'll study the
polyhedron, the cylinder, the cone, and the sphere.
Polyhedrons are space figures with flat surfaces, called faces, which are made of polygons. Prisms and pyramids are
examples of polyhedrons.
Cylinders, cones, and spheres are not polyhedrons, because they have curved, not flat, surfaces. A cylinder has two
parallel, congruent bases that are circles. A cone has one circular base and a vertex that is not on the base. A sphere is
a space figure having all its points an equal distance from the center point.
The space that we live in have three dimensions: length, width, and height. Three-dimensional geometry,
or space geometry, is used to describe the buildings we live and work in, the tools we work with, and the objects we
create.
First, we'll look at some types of polyhedrons. A polyhedron is a three-dimensional figure that has
polygons as its faces. Its name comes from the Greek "poly" meaning "many," and "hedra," meaning "faces." The ancient
Greeks in the 4th century B.C. were brilliant geometers. They made important discoveries and consequently they got to
name the objects they discovered. That's why geometric figures usually have Greek names!
We can relate some polyhedrons--and other space figures as well--to the two-dimensional figures that we're already
familiar with. For example, if you move a vertical rectangle horizontally through space, you will create a rectangular or
square prism.
If you move a vertical triangle horizontally, you generate a triangular prism. When made out of glass, this type of prism
splits sunlight into the colors of the rainbow.
Now let's look at some space figures that are not polyhedrons, but that are also related to familiar two-dimensional
figures. What can we make from a circle? If you move the center of a circle on a straight line perpendicular to the circle,
you will generate a cylinder. You know this shape--cylinders are used as pipes, columns, cans, musical instruments, and
in many other applications.
A cone can be generated by twirling a right triangle around one of its legs. This is another familiar space
figure with many applications in the real world. If you like ice cream, you're no doubt familiar with at least one of them!
A sphere is created when you twirl a circle around one of its diameters. This is one of our most common
and familiar shapes--in fact, the very planet we live on is an almost perfect sphere! All of the points of a sphere are at
the same distance from its center.
There are many other space figures--an endless number, in fact. Some have names and some don't. Have
you ever heard of a "rhombicosidodecahedron"? Some claim it's one of the most attractive of the 3-Dimensional figures,
having equilateral triangles, squares, and regular pentagons for its surfaces. Geometry is a world unto itself, and we're
just touching the surface of that world. In this unit, we'll stick with the most common space figures.

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At the end of the workbook, students are expected to:

1. define what polygon is;

2. know the different formulas in areas of polygons, surface areas and
volumes of space figures;

3. exercise the ability of the student in solving problem;

4. solve the areas of polygons;

5. solve the surface areas and volumes of space figures;

6. develop the skills of the students in solving problems involving different
formulas;

7. solve practical problems dealing with the different formulas in polygons
in easy way and less hour; and

8. formulate their own formulas in getting the areas of polygons, surface
areas and volumes of space figures.

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Vision, Mission, Goals and Objectives of College of Education
Foreword
Acknowledgement
Introduction
General Objectives
Table of Contents
Polygon
ACTIVITY
1 - 5 POLYGON
6 - 9 DIAGONALS OF A POLYGON
10 - 15 PERIMETER OF POLYGONS
16 - 17 ANGLES OF A POLYGON
18 - 21 REGULAR POLYGONS
22 - 24 SIMILARPOLYGONS
AREA OF POLYGONS
ACTIVITY
25 - 29 AREA OF RECTANGLES
30 - 34 AREA OF SQUARES
35 - 38 AREA OF PARARELLOGRAMS
39 - 41 AREA OF TRIANGLES
42 - 44 AREA OF TRAPEZOIDS
SURFACE AREA OF SPACE FIGURES
ACTIVITY
45 - 48 SURFACE AREA OF PRISM
49 - 53 SURFACE AREA OF PYRAMID
54 - 57 SURFACE AREA OF SIMILAR SOLID
58 - 62 SURFACE AREA OF SPHERE
63 - 64 SURFACE AREA OF CONE AND CYLINDER
VOLUME OF SPACE FIGURES
ACTIVITY
65 - 69 VOLUME OF PRISM
70 - 74 VOLUME OF PYRAMID
75 - 78 VOLUME OF SPHERE
79 - 83 VOLUMES OF CONE AND CYLINDER
References
Demo
Slideshare
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Part I

“To think the thinkable – that is
the mathematicians’ aim! “
E.J Keyser

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Name:_______________________________ Score: ____
Year/section: ____________ Date: _____

ACTIVITY 1

Instruction: Define the following terms.

1. Polygon 6.n-gon

2. Vertex of a polygon 7.nonagon

3. Side of a polygon 8.equilateral

4. Concave polygon 9.equiangular

5. Convex polygon 10.regular polygon

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Name:_______________________________ Score: ____

ACTIVITY 2

Instruction: Identify the polygons on the given figures. Give the reason why the others are not. Write the
answers at the back of this page

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

13. 14. 15.

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Name:_______________________________ Score: ____

ACTIVITY 3

Instruction: Classify each polygon by the number of sides and write if each is concave or convex.

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

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Name:_______________________________ Score: ____

ACTIVITY 4

Instruction: Find the measure of each interior angle of a regular polygon given the following. How many
sides does the polygon have?

1. 612˚

2. 120˚

3. 160˚

4. 165˚

5. 45˚

6. 10˚

7. 72˚

8. 90˚

9. 30˚

10. 180˚

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Name:_______________________________ Score: ____

ACTIVITY 5

Instruction: Draw each of the following polygon at the right side of this page.

1. A convex polygon with 5 sides.

2. A concave polygon with 9 sides.

3. Hexagon ABCDEF with AB=BC.

4. A concave polygon PORSTUVW.

5. Triangle ABC with AB=AC.

6. Pentagon RSTUV.

7. Quadrilateral WXYZ.

8. Octagon ABCDEFGH.

9. A Convex polygon with 8 sides.

10. A concave polygon with 4 sides.

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Name:_______________________________ Score: ____

ACTIVITY 6

Instruction: Find the number of diagonals in each polygon.

1. 15-gon 11. 70-gon

2. 18-gon 12. 18-gon

3. 27-gon 13. 68-gon

4. 70-gon 14. 41-gon

5. 100-gon 15. 200-gon

6. 50-gon 16. 405-gon

7. 64-gon 17. 40-gon

8. 81-gon 18. 83-gon

9. 94-gon 19. 1000-gon

10. 75-gon 20. 99-gon

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Name:_______________________________ Score: ____

ACTIVITY 7

Instruction: Find the number of diagonals in each of the following polygons

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

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Name:_______________________________ Score: ____

ACTIVITY 8

Instruction: Determine the number of sides of the following polygons, given the number of diagonals.

1. 275 diagonals

2. 405 diagonals

3. 60 diagonals

4. 90 diagonals

5. 150 diagonals

6. 35 diagonals

7. 50 diagonals

8. 100 diagonals

9. 80 diagonals

10. 40 diagonals

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Name:_______________________________ Score: ____

ACTIVITY 9

Instruction: Complete the table below.

Numbers of sides of Number of diagonals from Total number of diagonals
polygons each vertex

3

4

5

6

7

8

9

10

11

12

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Name:_______________________________ Score: ____

ACTIVITY 10

Instruction: Give the perimeter of the following polygon

1. 2. 3.
11 cm 3 cm 2 inch.
9 cm

5 cm 8 cm

4. 5.

3 in
4 cm

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Name:_______________________________ Score: ____

ACTIVITY 11

Instruction: Write T if the statement is correct and F if the statement is wrong.

1. 25 in + 10 in +15 in = 45 inches

2. 100 m + 110 m +121 m= 100 meters

3 .50 cm +50 cm +50 cm =150 cm

4. 2 km + 5 km + 7 km + 9 km = 20 km

5. 1.2 ft + 15 ft + 20 ft + 5 ft + 3 ft = 21 ft

6. 30 in + 50 in + 40 in + 60 in + 20 in = 200 in

7. 25 m +25 m + 25 m +25 m = 75 m

8. 45 cm + 63 cm + 70 cm + 80 cm = 150 cm

9. 1 km + 2 km + 3 km + 4 km + 5 km = 15 km

10. 90 in + 90 in + 90 in = 90 in

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Name:_______________________________ Score: ____

ACTIVITY 12

Instruction: First, estimate the perimeter of each polygon in centimeter. Then measure its sides in
centimeter to find the actual perimeter.

1. 2. 3.

4. 5. 6.

7. 8. 9.

10.

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Name:_______________________________ Score: ____

ACTIVITY 13

Instruction: Find the perimeter of each polygon with the following lengths of sides.

1. 4 cm, 6 cm, 7 cm

2. 72, 59, 96

3. 29.1 ft, 69.3 ft, 55.5 ft

4. 5. 60 in, 50 in, 40 in

5. 90 m, 95 m, 80 m

6. 4 yd, 2 yd, 6 yd, 8 yd

7. 8, 6, 9, 10, 11

8. 10 km, 13 km, 45 km, 50 km

9. 15 cm, 9 cm, 22 cm

10. 10 ft, 20 ft, 30 ft

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Name:_______________________________ Score: ____

ACTIVITY 14

Instruction: The following are the lengths of the sides of polygons, find the perimeter and match column A
to column B.

Column A Column B

____1. 5+ 6 + 7 =? a. 31

____2. l = 8, w = 2 b. 30

____3. s = 6 c. 20

____4. 2 + 3 + 3 + 4 =? d. 36

____5. 2.4 + 3.3 + 3 + 4.4 =? e. 18

____6. 9 + 8 + 7 + 5 + 6 =? f. 12

____7. 112 + 150 + 180 + 188 + 10 =? g. 24

____8. 3 + 5 + 6 + 8 + 9 =? h. 13.1

____9. 5.4 + 6.6 +11 + 13 =? i. 35

____10. 15 + 17 + 18 =? j. 640

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Name:_______________________________ Score: ____

ACTIVITY 15

Instruction: Find the sum of the interior angles of each polygon.

1. Decagon 6. Octagon

2. 40-gon 7. 38-gon

3. 100-gon 8. 200-gon

4. 267-gon 9. 320-gon

5. 800-gon 10. 903-gon

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Name:_______________________________ Score: ____

ACTIVITY 16

Instruction: The sum of the measures of the interior angles of the polygons are given below, find the
possible number of sides of each.

1. 2700˚ 11. 500˚

2. 3000˚ 12. 450˚

3. 1200˚ 13. 180˚

4. 1115˚ 14. 200˚

5. 1500˚ 15. 199˚

6. 250˚ 16. 924˚

7. 1595˚ 17. 2450˚

8. 587˚ 18. 1973˚

9. 667˚ 19. 388˚

10. 769˚ 20. 472˚

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Name:_______________________________ Score: ____

ACTIVITY 17

Instruction: Solve the following.

1. One angle of a rhombus is 88. What are the measures of the exterior angles?

2. A polygon has 22 sides. Find the sum of the measure of the exterior angles.

3. An interior angle of a regular polygon is 120. How many sides does the polygon have?

4. The measure of each interior angle of a regular polygon is 8 times that of an exterior angle. How many

5. In heptagon, the sum of the six exterior angles is 297. What is the measure of 7 th exterior angle?

6. The sum of the angles of polygon is 1620. How many sides does the polygon?

7. What is the measure of each interior angles of a regular 20-sided polygon?

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Name:_______________________________ Score: ____

ACTIVITY 18

Instruction: Choose the letters that corresponds to the interior and exterior angles of the regular polygons
given below. Write your answers opposite the given polygons.

Interior angles: a.156˚ b.144˚ c. 150˚ d.135˚ e. 108˚

Exterior angles: f.36˚ g.45˚ h.30˚ i.72˚ j.24˚

1. Regular pentagon

2. Regular 15-gon

3. Regular 12-gon

4. Regular octagon

5. Regular decagon

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Name:_______________________________ Score: ____

ACTIVITY 19

Instruction: You are given the number of sides of the polygon. Find the measure of each interior and exterior
angles.

1. 6 11. 35

2. 7 12. 47

3. 15 13. 32

4. 25 14. 3

5. 11 15. 10

6. 13 16. 19

7. 8 17. 30

8. 5 18. 50

9. 2 19. 4

10. 9 20. 23

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Name:_______________________________ Score: ____

ACTIVITY 20

Instruction: Find the measure of each interior angle of these polygons. Then find the sum of the measures of
the angles in each polygon.

1. Hexagon 6. Pentagon

2. Triangle 7. Quadrilateral

3. Heptagon 8. Nonagon

4. 20-gon 9. 50-gon

5. 100-gon 10. 1000-gon

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Name:_______________________________ Score: ____

ACTIVITY 21

Instruction: You are given the measure of the exterior and interior angles of a regular polygon. How many

Exterior angle of polygon

1. 162˚

2. 120˚

3. 160˚

4. 165˚

5. 90˚

Interior angle of polygon

1. 50˚

2. 25˚

3. 30˚

4. 520˚

5. 82˚

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Name:_______________________________ Score: ____

ACTIVITY 22

Instruction: The polygons shown are similar. Find the length of the sides denoted by x.

1. 2.

4
x
6
x
8

21
6
15

3. 4.
x
12
6
2
6
10
5
8 x
7

8
8. x
3
5

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Name:_______________________________ Score: ____

ACTIVITY 23

Instruction: Answer the following questions. Give the reason.

1. Are all squares similar?

2. Are all rectangles similar?

3. Are all equilateral triangles similar?

4. Two rhombuses each has 60˚ angle. Must they be similar?

5. Two isosceles trapezoids each has 100˚ angle. Must they be similar?

6. The length and width of one rectangle are each 2cm more than the length and width of another rectangle.
Are they similar?

7. If two figures are congruent, are they also similar?

8. If two figures are similar, are they also congruent?

9. Are equiangular triangles similar?

10. The length and width of a rectangle are 20 cm and 15cm respectively. Is a rectangle whose length and
width are 12cm and 9cm respectively, similar to the given rectangle?

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Name:_______________________________ Score: ____

ACTIVITY 24

Instruction: Solve the following problems.

1. Two isosceles triangles are similar and the ratio of corresponding sides is 3 to 5. If the base of the
smaller triangle is 18cm, find the base of the bigger triangle.

2. Given two similar triangles, triangle UST and triangle PLU with US = 8 cm, ST = 12 cm and UT = 16cm. If
PL = 12 cm, find the lengths of the other two sides.

3. What is the length of longer leg of a triangle whose shorter leg is 24 cm, if the ratio of the shorter leg to
the longer leg of a similar triangle is 5/6?

4. A copier machine is to reduce a diagram to 75% of its original size. The size of rectangle in the diagram
after it has been reduced is 9 cm by 12 cm. What are the dimensions of the bigger rectangle?

5. Stan and Gina created a design 6 inches by 8 inches for a piece of cloth that is 1 ft wide. They plan to
cross-stitch the same design on a piece of cloth that is 18 inches wide. What should be the measurement of
the new design?

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Part II

“A mathematical problem should be difficult in
order to entice us, yet not completely inaccessible,
lest it mock at our efforts. “
David Hilbert

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Name:_______________________________ Score: ____

ACTIVITY 25

Instruction: Find the area of each rectangle using the given measures.

1. b = 7 km , h = 14 km 6. b = 2.6 cm , h
= 5 cm

2. b = 7 cm , h = 1.5 cm 7. b = 21 ft , h =
12 ft

3. b = 18 yd , h = 9 yd 8. b = 3.75 ft , h
= 4.5 ft

4. b = 9.5 in , h = 9 in 9. b = 31 mm , h
= 23 mm

5. b = 13 km , h = 8 km 10. b = 11 dm ,
h = 6 dm

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Name:_______________________________ Score: ____

ACTIVITY 26

Instruction: Find the length of the base of each rectangle.

1. A = 56 cm2 , h = 7 cm 6. A = 416 mm2 , h = 52 mm

2. A = 63 cm2 , h = 9 cm 7. A = 117 dm2 , h = 13 dm

3. A = 180 m2, h = 15 m 8. A = 81 in2 , h = 27 in

4. A = 96 ft2 , h = 98 ft 9. A = 60 km2 , h = 5 km

5. A = 100 in2, h = 25 in 10. A = 160 yd2 , h = 16 yd

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Name:_______________________________ Score: ____

ACTIVITY 27

Instruction: Answer the following problems.

1. The measure of a basketball court is 26 cm by 14 cm, find its area.

2. Find the area of a baseball court with the measure of 90 ft by 60 ft.

3 . One face of chalk box has a length 60 cm and its width is 30 cm, find its area.

4. If the measure of a volleyball court is 50ft by 70 ft, what is area.

5. The measure of a floor is 26 m by 78 m, find its area.

6. Find the floor area of the gymnasium whose length and width is 65 m and 45 m respectively.

7. A badminton court has a measure of 27 m by 36 m, find its area.

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Name:_______________________________ Score: ____

ACTIVITY 28


1. Find the length of the base of a rectangle with the area of 186 square yards and a length of the altitude of
13 yards.

2. One dimension of rectangular pool table is 76 cm. Its area is 8664 cm 2, find the other dimension.

3. The length of the base of the table in the canteen is 15 m and the length of the diagonal is 17 m. Find its
area.

4. Find the area of a rectangle if the length of the base is 5 m and the length of the diagonal is 13 m.

5. Find the area of a rectangle ABCD where AB = 5 cm and BC = 8 cm.

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Name:_______________________________ Score: ____

ACTIVITY 29

Instruction: Find the area of each rectangle.
1. 5.

9 cm 9 yd

5 cm 7 yd

2. 8m 6.
18 m
2m

12 m

3. 7.
12 mm 4 cm

3 mm
13 cm

4. 8.
37 dm
5 cm

1 cm 17 dm

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Name:_______________________________ Score: ____

ACTIVITY 30

Instruction: Find the area of each square given the length of each side.

1. s = 4 m 6. s = 3 ft

2. s = 11 cm 7. s = 10 in

3. s = 12 mm 8. s=8m

4. s = 20 dm 9. s = 13 cm

5. s = 6 km 10. s = 5 km

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Name:_______________________________ Score: ____

ACTIVITY 31

Instruction: Find the length of the side of each square.

1. A = 16 m2 6. A = 46.24 in2

2. A = 144 cm2 7. A = 576 mm2

3. A = 25 km2 8. A = 6.25 km2

4. A = 81 in2 9. A = 49 cm2

5. A = 225 mm2 10. A = 100 ft2

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Name:_______________________________ Score: ____

ACTIVITY 32


1. A baseball diamond has a measure of 90 ft by 90 ft, find its area.

2. The square table of the teacher measures 65 cm by 65 cm, find its area.

3. If a softball diamond measures 78 ft by 78 ft, find its area.

4. Louie„s billboard has a measure of 15 m by 15 m, find its area.

5. A table tennis court measures 60 ft by 60 ft, find its area.

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Name:_______________________________ Score: ____

ACTIVITY 33


1. How many 6 – inch square bricks are needed to fill in a square window frame whose area is 900 sq. in.?

2. Find the dimension of a square field whose area is 196 square meters.

3. The area of a square is 675 cm2. Find the length of its side.

4. The coordinates of the vertices of a square are (0 , 5), (5, 0), (0 , - 5) and ( - 5, 0). What is the area of th
square?

5. Find the area of a square LOVE with LO = 10 cm and OV = 10 cm.

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Name:_______________________________ Score: ____

ACTIVITY 34

Instruction: Find the area of each square.
1. 5.
9.5 km

21 cm

2. 6.
3.75 cm 17 dm

3. 7.
8.3 Dm
18 in

4. 8.
8 cm
31 ft

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20.2 cm

Name:_______________________________ Score: ____

ACTIVITY 35

Instruction: The base and height of each parallelogram are given, find its area.

1. b = 7 km , h = 18 km 6. b = 120 cm , h = 70 cm

2. b = 5 km , h = 2 km 7. b = 3 ft , h = 14 ft

3. b = 70 in , h = 59 in 8. b = 8 ft , h = 4 ft

4. b = 25 m , h = 35 m 9. b = 75 mm , h = 34 mm

5. b = 2.5 km , h = 6.25 km 10. b = 5 dm , h = 36 dm

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Name:_______________________________ Score: ____

ACTIVITY 36

Instruction: Find the length of the base of each parallelogram.

1. A = 84 cm2 , h = 7 cm 6. A = 55 mm2 , h = 11 mm

2. A = 60 cm2 , h = 10 cm 7. A = 54 dm2 , h = 9 dm

3. A = 135 m2, h = 15 m 8. A = 65 in2 , h = 13 in

4. A = 147 ft2 , h = 21 ft 9. A = 36 km2 , h = 4 km

5. A = 30 in2, h = 3 in 10. A = 84 yd2 , h = 14 yd

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Name:_______________________________ Score: ____

ACTIVITY 37

Instruction: Find the area of each parallelogram.
1. 3.

5 cm
15 ft

13 cm
9 ft

2. 4.

7 cm
7m
8.5 cm

3m

3. 6.

5 in
3 mm

15 in
7 mm

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Name:_______________________________ Score: ____

ACTIVITY 38

Instruction: Supply the missing number where b is the base, h is the height and A is the area.

b h A

1.
8 14 ?

2.
7 ? 91

3.
1.2 5 ?

4.
? 6 48

5
10 ? 90

6.
15 12 ?

7.
? 7 84

8.
19 ? 57

9.
20 5 ?

10.
70 58 ?

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Name:_______________________________ Score: ____

ACTIVITY 39

Instruction: Find the area of each triangle using the given measures.

1. b = 6 cm , h = 4cm 6. b = 13 dm , h = 10 dm

2. b = 8 m , h = 4 m 7. b = 8 yd , h = 5 yd

3. b = 10 ft , h = 5 ft 8. b = 4 km , h = 2 km

4. b = 14 in , h = 6 in 9. b = 16 cm , h = 15 cm

5. b = 11 m , h = 8 m 10. b = 21 mm , h = 14 mm

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Name:_______________________________ Score: ____

ACTIVITY 40

Instruction: Find the length of the base of each triangle.

1. A = 72 cm2 , h = 12 cm 6. A = 72 mm2 , h = 9 mm

2. A = 15 m2 , h = 2.5 m 7. A = 40 dm2 , h = 10 dm

3. A = 12 km2, h = 18 km 8. A = 92 in2 , h = 4 in

4. A = 484 ft2 , h = 4 ft 9. A = 50 km2 , h = 5 km

5. A = 7.2 in2, h = 0.6 in 10. A = 8 yd2 , h = 4 yd

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Name:_______________________________ Score: ____

ACTIVITY 41

Instruction: Find the area of each triangle.
1. 4.

5m 9 mm

8 mm

2. 5.

7cm
2.4 m

13 cm
3.1 m

3. 6.

5m 9m
6m
45 m
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ACTIVITY 42

Instruction: Find the area of each trapezoid using the given measures.

1. b1 = 6 mm , b2 = 12 mm , h = 410 mm 6. b1 = 25 cm , b2 = 17 cm , h = 41 cm

2. b1 = 12 m , b2 = 3 m , h = 3 m 7. b1 = 6 yd , b2 = 8 yd , h = 4 yd

3. b1 = 32 in , b2 = 15 in , h = 9 in 8. b1 = 7 km , b2 = 21 km , h = 10 km

4. b1 = 76 mm , b2 = 34 mm , h = 44 mm 9. b1 = 62 in , b2 = 432 in , h = 410 in

5. b1 = 65 dm , b2 = 5 dm , h = 4 dm 10. b1 = 3 ft , b2 = 2 ft , h = 6 ft

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Name:_______________________________ Score: ____

ACTIVITY 43

Instruction: Find the area of each trapezoid.
1. 4. 3m
3m

2.5 m 2m

7.25 m
7m

2. 5.

18 cm

6 cm
5 ft 10 ft
3 ft
25 cm

3. 6.
10 ft

4 ft 14 in

23 in 5 in

5 ft

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Name:_______________________________ Score: ____

ACTIVITY 44

Instruction: In exercises 1 – 8 the b1 and b 2 are the base, h is the altitude and A is the area of trapezoid.
Supply the missing measure.

b1 b2 h A

12 cm 4 cm 7 cm ?
1.

8m 5m 3m ?
2.

7 mm 3 mm ? 40 mm
3.

12 km 8 km ? 44 km
4.

? 3 dm 3 dm 12 dm
5.

6 ft ? 4 ft 28 ft
6.

5 3 ?
7.

5 ? 4t 52
8.

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Part III

“The purpose of computation is
insight, not numbers!”
Richard Hamming

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Name:_______________________________ Score: ____

ACTIVITY 45

Instruction: Match column A from column B.

B
A
D
C

x
E

G
F
H
A B

Base of prism a. x

Lateral face of prism b. EFTFG+GH+EH

Height of prism c.- ADHE

Slant height of prism d. AE

Perimeter of a base e. EFGH

Lateral edge of prism f. CG

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ACTIVITY 46

Instruction: Solve for the lateral area of the following prism. Use the formula, LA= ph

1. p = 7 mm, 4 mm 6. p = 20 yd, 17yd, 28 yd
h = 6 mm h = 10 yd

2. p = 15 cm, 3 cm 7. p = 9 ft, 10 ft, 11 ft
h = 3 cm h = 15 ft

3. p = 10 cm, 8 cm, 6 cm 8. p = 5 cm, 10 cm
h = 5 cm h = 3 cm

4. p = 20 in, 5 in, 15 in 9. p = 9 in, 7 in
h = 5 in h = 5 in

5. p = 12 m, 15m, 7m 10. p = 3 m, 4 m
h=8m h=2m

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Name:_______________________________ Score: ____

ACTIVITY 47

Instruction: Supply the missing number where P is the perimeter, H is the height and LA is the lateral area
of prisms.

1.
P= 8 H = 10 LA =?
2.
P= 7 H=? LA = 35
3.
P =? H=6 LA = 36
4.
P =? H=9 LA = 72
5.
P = 72 H = 90 LA =?
6.
P = 21 H =? LA = 63
7.
P= 8 H =? LA = 64
8.
P= ? H = 90 LA = 180
9.
P = 75 H= 5 LA =?
10.
P = 200 H=4 LA =?

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Name:_______________________________ Score: ____

ACTIVITY 48

Instruction: Find the L.A and T.A for each right rectangular prism.

1.

12
2. 15

9
10
10

9
3. The perimeter of the base of a right prism is 12cm and the height is 6cm. Find

the L.A..
9
4. The perimeter of the base of a right prism is 8m and the height is 3m. Find the L.A.

5. Find the L.A. and the T.A. of the cube.

5cm

6. The edge of a cube is 7cm. find the L. A. and T.A.

7. The perimeter of the base of a cube is 16cm. Find the T.A.

8. The perimeter of the base of a cube is 24m. Find the T.A.

9. Find the L.A. and T. A. of a right prism whose base is a square.

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Name:_______________________________ Score: ____

ACTIVITY 49

Instruction: Use the regular pyramid below to match column I to column II.

A

B
C

2

3
Column I Column II

1. Base a. BCE
2. Area of base b. 4
3. Lateral Face c. AD
4. Height d. ABCD
5. Slant height e.
6. Base Edge f. E
7. Lateral Edge g. 4 square
unit
8. Surface Area h. 1 unit
9. Vertex i. (4+4 )
square units
10. Lateral Area j. EC
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Name:_______________________________ Score: ____

ACTIVITY 50

Instruction: Complete each statement with always, sometimes, or never.

1. The lateral faces of a pyramid are_________ triangle regions.

2. The number of lateral edges is _________ the number of vertices of the base of regular pyramid.

3. The lateral faces of a pyramid are _________ congruent.

4. The base of a regular pyramid is ___________ congruent.

5. The lateral faces of a regular pyramid are _________scalene triangles.

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Name:_______________________________ Score: ____

ACTIVITY 51

Instruction: Find the lateral area of the following regular prism.
1 4
base = 9cm base = 32m

height = 12cm height = 25m

2. 5.

base = 14cm base = 10 cm

height = 21cm height = 8 cm

3. 6.

base = 7cm base = 6m

height = 17cm height = 9m

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ACTIVITY 52

Instruction: Complete the table below.

SURFACE AREA LATERAL AREA BASE AREA

1. 380cm2 ? 100cm2

2. 100mm2 50mm2 ?

3. ? 45cm2 95cm2

4. ? 115cm2 85cm2

5. 1050m2 1000m2 ?

6. 2505c ? 2000cm2

7. 999cm2 99cm2 ?

8. ? 875m2 100m2

9. 1036m2 ? 1005m2

10. 25cm2 8cm2 ?

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ACTIVITY 53

Instruction: Find the total surface area of each polygon using the given conditions.

1. Regular pyramid, whose base is a square of side 10 inches and whose altitude is 12 inches.

2. A regular pyramid, whose base is a hexagon of side 10 inches and whose altitude is 20 inches.

3. Frustum of a regular square pyramid, whose base has sides 20 inches each long, respectively, and
whose altitude is 12 inches.

4. The base of square pyramid is 5 ft, the area of the base is 25 ft 2, the perimeter is 20 ft and the altitude is 4
ft.

5. The perimeter of the base is 34 cm and the altitude is 14 m.

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Name:_______________________________ Score: ____

ACTIVITY 54

Instruction: The space figures in each activity are similar. Find x. Then find the ratios of the corresponding
lengths and surface areas.
1. 4.

6
5
4
9
6 x
x
3
2. 5. 8 12

20
x 8 x

3 5

6
2
3. 6.

x
3 7 4

x 15

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ACTIVITY 55

Instruction: Solve the following problems. Use the figures at the right side.

1. The height of the smaller cylinder is 8. What 10 m
is the height of the larger cylinder?
5m

8m

2. The surface area of the larger cylinder is
288п. What is the surface area of the smaller
cylinder?

3. The diameter of the larger cylinder is 10. 10 m
What is the diameter of the smaller cylinder? 10 m

4. The surface area of the smaller cylinder is 5m 25 m
75п. What is the surface area of the larger
cylinder?

5. The radius of the smaller cylinder is 5. What
is the radius of the larger cylinder?

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Name:_______________________________ Score: ____

ACTIVITY 56

Instruction: Complete the table below showing the relative amount of surface area of some objects.

Objects Radius Surface Area

Ball 15 cm 1256cm2

1. Golf ball 4 cm ?

2. Billiard ball 5 cm ?

3. Soccer ball 14 cm ?

4. Marble 2 cm ?

5. Christmas ball 8 cm ?

6. Watermelon 18 cm ?

7. Quezo de bola 10 cm ?

8. Lollipop 1.5 cm ?

9. Atom 0.5x10-8 cm ?

10. Earth 3950 miles ?

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Name:_______________________________ Score: ____

ACTIVITY 57

Instruction: Draw the solid, and then find its surface area.

1. Larger rectangular prism: length = 8 cm, width =12 cm, height = 18 cm
Smaller rectangular prism: length = 4 cm, width =8 cm, height = 14 cm

2. Larger cylinder: radius = 3.5 inch, height = 8 inch
Smaller cylinder: radius = 2 inch, height = 4 inch

3. Larger right circular cone: radius =? , height = 10 cm
Smaller right circular cone: radius =3 cm, height = 5 cm

4. Larger sphere: radius = 11cm
Smaller sphere: radius = 6 cm

5. Larger rectangular box: length = 12 cm, width =6 cm, height =?
Smaller rectangular box: length = 6 cm, width =3 cm, height = 7 cm

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ACTIVITY 58

Instruction: Find the surface area of a sphere with the given measures.

1. 4cm

2. 1.3cm

3. 2.1cm

4. 9m

5. 7m

6. 3.7m

7. 1.5m

8. 8.7cm

9. 3.5cm

10. 19inch
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Name:_______________________________ Score: ____

ACTIVITY 59

Instruction: Match column A to column B.

A B

1. 9 m a. 400п m 2

2. 10 m b. 810 m

3. 8m c. 1444п m 2

4. 3.5 m d. 100п m 2

5. 6 m e. 256п m 2

6. 5 m f. 4752п m 2

7. 19 m g. 49п m 2

8. 109 m h. 1000п m 2

9. 50 m i. 196п m 2

10. 7 m j. 144п m 2

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Name:_______________________________ Score: ____

ACTIVITY 60

Instruction: A sphere has radius r, diameter d and circumference c of a great circle. Fill in the blanks.

Radius Diameter Surface area

1. ________ _______ 2916п

2. 40 _______ ______

3. _______ _______ 1936п

4. _______ _______ 196п

5. 5 _______ ______

6. ________ 100 ______

7. ________ _______ 265п

8. 2 _______ _______

9. ________ 10 _______

10. 9 _______ _______

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ACTIVITY 61

Instruction: Find the surface area of the sphere, given the following.

1. r = 70 cm

2. d = 1.2 m

3. d = 60 cm

4. d = 22 m

5. r = 50 m

6. r = 1.5 mm

7. d = 500 m

8. d = 7 cm

9. r = 8 mm

10. d = 69 m

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ACTIVITY 62

Instruction: Solve the following.

1. The surface area of a great circle of a sphere is 6900 cm2 .What is the surface area of the sphere?

2. The surface area of the great circle of a sphere is 1m2.What is the area of the sphere?

3. The area of a sphere is 476m2 .What is the surface area of a great circle of the sphere?

4. A soccer ball has a diameter 0f 9.6 inches. Find the surface area of the sphere.

5. Consider the earth as a sphere with a radius of 4000 miles. Find its surface area.

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Name:_______________________________ Score: ____

ACTIVITY 63

Instruction: Find the surface area of each figure.
1. 2. 3.
12 cm
6m
4.25 m
2m 18 cm
7m

4. 5. 6 inches 6.

4 cm
15 cm
12 cm
14 inches
7 cm

7. 8. 9.
6m
6 inches
20 cm
10 m

8 inches 8 cm
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ACTIVITY 64


1. The height of a right circular cylinder is 20 cm and the radius of the base is 10 cm. Find the total area.

2. The height of a right circular cylinder is 10 cm and the diameter of the base is 18 cm. Find the lateral
area.

3. A cylinder tank can hold 1540 m3 of H2O is to be built on a circular base with the diameter of 7 m. What
must be the height of the tank?

4. A right circular cylinder has a lateral area of 2480 cm2. If the height of the cylinder is 16 cm, what is the
radius of the base?

5. Find the total area of a right circular cylinder having a height of 5 m and the base has a radius of 1.5 m.

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Part IV

“The intelligence is proved not by ease of learning,
but by understanding what we learn. “
Joseph Whitney

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Name:_______________________________ Score: ____

ACTIVITY 65

Instruction: Find the volume of each prism. The area of the base B and the height h are given.

1. B = 24 cm2 , h = 5 cm

2. B = 64 yd2 , h = 27 yd

3. B = 28 m2 , h=6m

4. B = 50 cm2 , h = 10 cm

5. B = 58 mm2 , h = 4 mm

6. B = 75 ft2 , h = 15 ft

7. B = 175 m2 , h = 25 m

8. B = 250 cm2 , h = 30 cm

9. B = 296 mm2 , h=9m

10. B = 1292 ft2 , h = 5cm

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ACTIVITY 66

Instruction: Use the following information to answer the questions that follow.

1. A brown paper lunch bag is 3 ⅛ x 5 ⅛ x 10 ¼. A brown paper grocery bag is 7 x 11 ½ x 17.

2. Find the volume of the lunch bag.

3. Find the volume of the grocery bag.

4. Approximate the ratio of the volume of the lunch bag.

5. Are two bags similar? Explain.

_______________________________________________________________________________________________________________________
_______________________________________________________________________________________________________________________
_______________________________________________________________________________________________________________________
_______________________________________________________________________________________________________________________
_______________________________________________________________________________________________________________________
_______________________________________________________________________________________________________________________
_______________________________________________________________________________________________________________________
_______________________________________________________________________________________________________________________
________________________________________________.

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ACTIVITY 67

Instruction: Find the volume of each figure.

1. 2. 3.

6 cm 20 cm
8 cm
3 cm
4 cm
10 cm 8 cm
2 cm 35 cm

4. 5. 6.

10 cm
4 cm
9 inch.

0.8 m 10.6 m
11 inch.
3.2 m
23 inch.
7. 8. 9.

3 ft
4 cm
11 m
1.5 ft
7 cm
2 ft
6m
5 cm 18 m

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ACTIVITY 68

Instruction: Match each item with the best estimated volume.

1. Swimming pool
a. 120 cm3
2. Soap box b. 750 cm3

3. Test tube c. 380 m3
4. Bar soap d. 500 mm3

Complete the statements with the most appropriate units (m3, cm3, mm3)

1. The volume of a 10-gallon fish tank is about 40___.

2. The volume of a gymnasium is about 30,000___.

3. The volume of a refrigerator is about 30,000___.

4. The volume of a ca condensed milk is about 354 ___.

5.v The volume of a an allergy capsule is about 784___

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ACTIVITY 69


1. How many cubic meters of concrete will be needed for a ratio 12 m long, 8 m wide, and 12cm deep?

2. A prism has a square base and a volume of 570 cm3, if it is 9 cm high, how long is a side of a base?

3. Find the volume of a regular triangle prism whose height is 15 cm and whose base has side that each
measure 20 cm.

4. Find the volume of a prism whose base has an area of 24 cm2 and whose height is 8 cm.

5. Find the volume of a prism with a trapezoidal base and a height of 35 cm. The lengths of the parallel sides
of the trapezoid are 40 cm and 95 cm. The altitude of the trapezoid is 5 cm.

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ACTIVITY 70

8in
Instruction: Find the volume of each pyramid.
1. 2.
7cm

6cm
4cm 5in 11in
4in

3. 4.
9ft
11m

13.5ft
9m
14m
17ft

5.
3ft

4ft
6.5ft

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ACTIVITY 71

Instruction: Solve the following word problems.

1. The great pyramid in Egypt is approximately 137 m tall, the square base measures 225 m on each edge.
Find the volume of the pyramid.

2. The area of the base of a pyramid is 237 cm2, and the height of the pyramid is 1 m. Find the volume in
cubic centimeters.

3. The height of the pyramid is 15 ft, the base is a right triangle whose legs is 9 in and 12 in long. Find the
volume of the pyramid in cubic inches.

4. A regular pyramid has a base area of 289 ft2 and a volume of 867 ft. What is the height of the pyramid?

5. If the area of the base of a pyramid is doubled, how does that affect the volume?

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Name:_______________________________ Score: ____

ACTIVITY 72

Instruction: Find the height of the pyramid. The area of the base B and the volume of pyramid V are given.

1. B = 16.5 m2 V = 330 m3

2. B = 27 cm2 V = 49.5 cm3

3. B = 229 in2 V = 688.5 in3

4. B = 105 yd2 V = 350 yd3

5. B = 16 m2 V = 21.33 m3

6. B = 80 cm2 V = 106.67 cm3

7. B = 289 ft2 V = 867 ft3

8. B = 1995 ft2 V = 6650 ft3

9. B = 30 m2 V = 50 m3

10. B = 300 mm2 V = 800 mm3

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Name:_______________________________ Score: ____

ACTIVITY 73

Instruction: Given the area of the base and height, find the volume of the pyramid.

1. B = 25 cm2, h = 3 cm 6. B = 48 ft2 , h = 7 ft

2. B = 52 m2, h = 9 m 7. B = 95 in2 , h = 6 in

3. B = 62 in2, h = 5 in 8. B = 85 yd2 , h = 7 yd

4. B = 77 mm2, h = 5 mm 9. B = 115 mm2 , h = 12 mm

5. B = 89 m2, h = 15 m 10. B = 69 m2 , h = 8 m

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Name:_______________________________ Score: ____

ACTIVITY 74

Instruction: Use mathematical reasoning in answering the following questions.

1. A regular pyramid has the base area of 389 ft2 and a volume of 867 ft2. What is the height of the pyramid?

2. Two regular pyramids have square bases and equal heights. If the length of a side of one of the bases is 1
m, and the length of a side of the other is 3 , how will the volumes compare?

3.

A cube is broken into six identical pyramids as shown. Each face of the cube is a base of a pyramid. An edge
of the cube is 10 cm. What is the volume of pyramid?

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ACTIVITY 75

Instruction: Find the volume of a sphere with the given radius.

1. 36 cm 6. 1.4 ft

2. 45 m 7. 5.6 yd

3. 2 km 8. 9.6 in

4. 1.5 m 9. 9 cm

5. 2.75 mm 10. 10.9 cm

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ACTIVITY 76


1. The radii of two spheres are 5 cm and 9.8 cm, respectively. What is the ratio of their volumes?

2. The diameters of two spheres are 12 m and 19 m, respectively. What is the ratio of their volumes?

3. A soccer ball has a diameter of 9.6 inches. Find its volume.

4. Find the volume of sphere whose radius is 15 cm.

5. Consider the earth as a sphere with the radius of 4000 miles, find its volume.

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ACTIVITY 77

Instruction: The diameters of spheres are given. Find its volume.

1. 68 mm 6. 14 dm

2. 24 m 7. 28 cm

3. 76 in 8. 12 ft

4. 56 yd 9. 6 km

5. 8 km 10. 22 in

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ACTIVITY 78

Instruction: Find the volume of spheres, given the radius.

1. r = 6 m 6. r = 16 cm

2. d = 18 in 7. d = 42 in

3. r = 17 cm 8. r = 7 m

4. r = 26 mm 9. r = 17 ft

5. d = 36 mm 10. d = 82 mm

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ACTIVITY 79

Instruction: Find the volume of each cone.
1. 2.

13 m
31 m

7m

12 m
3. 4.

2.3 cm
27 ft
5.2cm
12.5 ft

5.

2.3 cm

5.2cm

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ACTIVITY 80

Instruction: Find the volume of each cylinder.
1. 2.

5 cm 14 cm

9 cm 4m

3. 4.

16 ft 15 cm

15 ft 13 cm

5.
15 cm

13 cm
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