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Workbook in polygons and space figures

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  • 1. contents next
  • 2. 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. contents back next
  • 3. 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. contents back next
  • 4. 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. contents back next
  • 5. 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. contents back next
  • 6. 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 contents back next
  • 7. 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 contents back next
  • 8. 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 contents back next
  • 9. 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. contents back next
  • 10. 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. contents back next
  • 11. 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 contents back next
  • 12. Part I “To think the thinkable – that is the mathematicians’ aim! “ E.J Keyser contents back next
  • 13. 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 contents back next
  • 14. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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. contents back next
  • 15. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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. contents back next
  • 16. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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˚ contents back next
  • 17. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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. contents back next
  • 18. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 19. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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. contents back next
  • 20. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 21. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 22. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 23. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 24. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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. contents back next
  • 25. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 26. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 27. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 28. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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˚ contents back next
  • 29. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 sides does the polygon have? 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? contents back next
  • 30. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 31. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 32. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 33. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ ACTIVITY 21 Instruction: You are given the measure of the exterior and interior angles of a regular polygon. How many sides does the polygon have? 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˚ contents back next
  • 34. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 35. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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? contents back next
  • 36. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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? contents back next
  • 37. 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 contents back next
  • 38. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 39. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 40. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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. contents back next
  • 41. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ ACTIVITY 28 Instruction: Solve the following problems. 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. contents back next
  • 42. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 43. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 44. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 45. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ ACTIVITY 32 Instruction: Solve the following problems. 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. contents back next
  • 46. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ ACTIVITY 33 Instruction: Solve the following problems. 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. contents back next
  • 47. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next 20.2 cm
  • 48. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 49. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 50. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 51. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 ? contents back next
  • 52. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 53. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 54. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 55. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 56. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 57. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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. contents back next
  • 58. Part III “The purpose of computation is insight, not numbers!” Richard Hamming contents back next
  • 59. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 60. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 61. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 =? contents back next
  • 62. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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. contents back next
  • 63. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 64. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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. contents back next
  • 65. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 66. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 ? contents back next
  • 67. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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. contents back next
  • 68. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 69. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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? contents back next
  • 70. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 ? contents back next
  • 71. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 72. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 73. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 74. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 _______ _______ contents back next
  • 75. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 76. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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. contents back next
  • 77. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 78. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ ACTIVITY 64 Instruction: Solve the following problems. 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. contents back next
  • 79. Part IV “The intelligence is proved not by ease of learning, but by understanding what we learn. “ Joseph Whitney contents back next
  • 80. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 81. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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. _______________________________________________________________________________________________________________________ _______________________________________________________________________________________________________________________ _______________________________________________________________________________________________________________________ _______________________________________________________________________________________________________________________ _______________________________________________________________________________________________________________________ _______________________________________________________________________________________________________________________ _______________________________________________________________________________________________________________________ _______________________________________________________________________________________________________________________ ________________________________________________. contents back next
  • 82. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 83. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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___ contents back next
  • 84. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ ACTIVITY 69 Instruction: Solve the following problems. 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. contents back next
  • 85. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 86. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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? contents back next
  • 87. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 88. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 89. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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? contents back next
  • 90. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 91. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ ACTIVITY 76 Instruction: Solve the following problems. 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. contents back next
  • 92. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 93. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 94. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 95. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ 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 contents back next
  • 96. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ ACTIVITY 81 Instruction: Given the radius and diameter, find the volume of each cone. 1. r =8 cm, h = 13 cm 6. r =9 cm, h = 18 cm 2. r =8 m, h = 21.5 m 7. d =18 mm, h = 27 mm 3. d =15 in, h =17 in 8. d = 10 in, h = 50 in 4. d =25 ft, h = 15 ft 9. r =6 ft, h = 15 ft 5. r = 89 m2, h = 15 m 10. r =4 m, h = 12 m contents back next
  • 97. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ ACTIVITY 82 Instruction: If d stands for the diameter of each cylinder, find the volume. 1. d =28 m, h = 7m 6. d =69 cm, h = 32 cm 2. d =32 cm, h = 17.5 cm 7. d =58 mm, h = 26 mm 3. d =85 in, h =15 in 8. d = 62in, h = 43 in 4. d =12 ft, h = 15 ft 9. d =33 cm, h = 17 fcm 5. d = 84 mm, h = 18 mm 10. d = 6 dm, h = 15 dm contents back next
  • 98. Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ ACTIVITY 83 Instruction: Solve the following problems. 1. The volume of a circular cone is 1005 cm3 and the height is 25 cm, find the radius of the base. 2. A gas storage tank has a radius of 4 m and a height of 8 m, find the volume of the cylinder. 3. Find the volume of a right circular cylinder having a height 0f 60 m and with a base whose radius is 20 m. 4. The height of a circular cylinder is 180 in and the radius of the base is 90 in. Find the volume. 5. If the volume of a circular cylinder is 72 cm3 and the radius of the base is 90 cm, find the volume. contents back next
  • 99. References BOOKS Edelmira, Mapile (2005) . Geometry . Marikina City : Academe Publishing House, Inc. . Larson, Roland E. , & Stiff, Lee (1998) . Heath Geometry an Integrated Approach . United State : Heath and Company, A Division of Houghton Mifflin Company . Smith, Stanley A. , Nelson, Chares W. , Koss, Roberta K. , Mervin C. , & Bittinger, Marvin L. (1992) . Informal Geometry . United State : Addisson – Wesley Publishing Company Inc. . Malaborbor, Pastor B. , Sabangan, Leticia E. , & Lorenzo, Jose Ramon S. . Geometry . Quezon City : Educational Resources Corporation . Mercado, Jesus P. , Suzara, Josephine L. , & Orines, Fernando B. . Geometry . contents back next
  • 100. URL http://www.math.com/school/subject3/lessons/S3U4L1GL.html February 10, 2010 http://freespace.virgin.net/hugo.elias/graphics/x_polyd.htm February 10, 2010 http://en.wikipedia.org/wiki/Polygon February 10, 2010 contents back next
  • 101. Images 001 http://logos.simpleplants.com/Schools-Education/largeimages/Schools- Classroom-Activities-Boy_Studying.jpg February 1, 2010 002 http://images.clipartof.com/small/32965-Clipart-Illustration-Of-A- Happy-Brother-And-Sister- Reading-A-Yellow-Book-Together.jpg February 1, 2010 003 http://dclips.fundraw.com/pngmax/scissors.png February 1, 2010 004http://www.schoolclipart.net/images/illustrations/thumbnail/9371_schoolb oy_thinking_while_taking_a_test.jpg February 1, 2010 005 http://images.clipartof.com/small/42004-Clipart-Illustration-Of-A-Red- Haired-Little-Boy-Sitting-On-The-Floor-And-Reading-A-Story-Book.jpg February 1, 2010 006 http://math.pppst.com/banner_math_polygons.gif February 17, 2010 contents back next
  • 102. Jezreel Astejada Revellame is the eldest son of Mr. Emmanuel B. Revellame Sr. and Mrs. Eterna A. Revellame. He was born on February 13, 1992 at Infanta, Quezon. He finished his elementary in General Nakar Central School and finished his high school in Mount Carmel High School in General Nakar, Quezon. He finished his tertiary level in 2012 at Laguna State Polytechnic University with the Degree of Bachelor of Secondary Education major in Mathematics. Louie Magracia Magayon is the youngest son of Mr. Samuel M. Magayon and Mrs. Amalia M. Magayon. He was born on April 30, 1990 at San Agustin, Romblon. He finished his elementary in Pang- ala alang Paaralang Severina M. Solidum and finished his high school in Mabitac National High School. He finished his tertiary level in 2012 at Laguna State Polytechnic University with the Degree of Bachelor of Secondary Education major in Mathematics. contents back next

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