3 Chapter 2 Prism and Cylinder PDF

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Summary

The learner demonstrates understanding of key concepts of solids such as prism, cylindrical surface, circular cylinder, right circular cylinder,
right circular cylinder, pyramid, regular pyramid, similar figures, conical surface, cone, and right circular cone....

Description

MODULE 1 IN

SOLID MENSURATION A Message to the Learner

Dear Louisian, In the past few months, numerous things have happened which we did not expect. There are some things that we normally do before which are not possible now. There are also some things that we do not usually do before, but now these things seem to be the new normal. But one thing is for sure, whatever happens, your love for learning will always be there and should not be hampered. So, we, your Math teachers, have prepared a simple module for you. In this module, you will find sample problems with complete and step-by-step solutions, practice exercises, and other activities that will check your understanding of Solid Mensuration. Keep in mind that the more you practice solving, the more you get to understand the lesson. Happy learning! GENERAL INSTRUCTIONS: ✓ Download the module containing CHAPTER 1: Prism and Cylinder.

SUMMATIVE ASSESSMENTS ✓ Summative Assessments are labeled as AssessMath Time. If you have a printer, print the worksheet on a short bond paper, then answer it. If otherwise, on a short bond paper, copy everything including the title of the activity, instructions, given, then your answer. Scan your worksheet or take a clear picture of the entire worksheet and upload it in MS Teams. Please read and follow the GENERAL INSTRUCTIONS FOR SUBMISSION OF WORKSHEET VIA MS TEAMS. The date of submission will be on or before December 9, 2020. FORMATIVE ASSESSMENTS ✓ If you DO NOT HAVE a printer at home, the formative assessments must be answered in your notebook for compilation. It must be labeled following this format: module number, lesson number, the title of the activity, and your answers showing your complete solution (if asked). ✓ If you have a printer at home, you may print the formative assessments on a short bond paper. Compile them in a short brown envelope. ✓ Check your answers in every lesson. A key answer is also provided for you. You may download the key answer or just simply open the file for viewing. Write your scores in your notebook or your printed copy of the worksheet. 1 | Chapter 1. Prism and Cylinder

This module has the following parts and corresponding icons:

Learning Targets

This part enumerates the objectives of the module stated as “I can” statements. This part shall give you an idea of the skills or competencies you are expected to acquire upon completion of this module.

Warm-up Exercises

This serves as the motivation part of the module. It contains trivia, puzzle, game and/or other interesting activities that will make you excited to accomplish the module.

Math Lens

The discussion or lesson proper of the module is presented on this part. It contains simplified explanation of the topic with some practice exercises that you should try to answer.

Math Checkpoint!

These are the practice exercises included in various parts of the module to help you practice the things you have learned. This will also prepare you for the summative assessment referred to as AssessMath Time!

Math to Ponder!

This involves the reflective part of the module. It contains various activities that will allow you to reflect and state what you have learned. It will also give you an opportunity to ask question/s about some concepts presented in the module.

AssessMath Time!

This is the summative assessment presented on the latter part of each module. It is a graded assessment that will check how much have you learned from the module.

Math-in-Action

This part is where you will do your performance tasks. It contains authentic assessment/s, wherein you can put into action or apply in real-life situations the things that you have learned.

Confidentiality Notice: The module and any of its attachments are meant for the use of the learners who are enrolled in this subject. This module is for academic/school purposes only and is not meant for sharing, publishing, copying, and disseminating. Hence, the distribution of this module and any of its content/s is strictly prohibited. 2 | Chapter 1. Prism and Cylinder

Content Standards: The learner demonstrates understanding of key concepts of solids such as prism, cylindrical surface, circular cylinder, right circular cylinder, right circular cylinder, pyramid, regular pyramid, similar figures, conical surface, cone, and right circular cone.

Performance Standards: The learner is able to analyze, define, elaborate, solve accurately problems involving some solids, and create their own samples of these solids.

At the end of this module, I must be able to say the following with conviction: ✓ I can define a prism; ✓ I can enumerate the different properties of a prism; ✓ I can memorize the different formulas in solving for the lateral area; surface area and volume of a prism; ✓ I can solve real life problems involving prism; ✓ I can define a cylinder; ✓ I can enumerate the different properties of a cylinder; ✓ I can memorize the different formulas in solving for the lateral area; surface area and volume of a cylinder; and ✓ I can solve real life problems involving cylinder. Warm-up Exercises: Our brains should be treated like the muscles in our body, before doing a strenuous workout; we need to warm it up. Thus, solve the puzzle below before you start accomplishing the module.

The next line in this pattern is:

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MATH Lens

This module tackles Prism and Cylinder, try to accomplish this within 295 minutes. A timetable is provided below to help you manage your time properly. This module shall be submitted on December 9, 2020. Enjoy your learning escapade! 15 minutes 50 minutes 50 minutes 60 minutes 120 minutes

A. Definition A polyhedron of which 2 faces are equal polygons in parallel planes and the other faces are parallelograms. B. Properties of a Prism 1) Bases are equal and parallel polygons; 2) The lateral faces are all parallelograms ; 3) The lateral edges are equal and parallel; and 4) Prisms are named according to the shape of their bases. (Eg. Octagonal Prism, Triangular Prism, Hexagonal Prism)

C. Formulas in Calculating the Surface Area, Lateral Area and Volume of a Prism

Surface Area

SA = LA + 2B

Lateral Area

Volume

LA = 𝑷𝒉

V = Bh

P is the perimeter of the base

B is the area of the base

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MATH CHECKPOINT! Complete the table below by solving the missing values. Use the formula in computing or calculating the surface area, lateral area, and volume of a RECTANGULAR prism. Keep your paper clean and organized. (Total: 15 points) Width of the Prism (w)

Height of the Prism (h)

1. 10 cm

15 cm

20 cm

2. 6 in

13 in

14 in

3.

10 ft

25 ft

4. 13 dm

4 dm

Length of the Prism (l)

5. 4 in

Surface Area (SA)

Lateral Area (LA)

Volume (V)

1 000 ft3

442 dm3

6in

120 in2

D. Word Problems Involving Prism Read and analyze each item below, then solve what is being asked. Show your COMPLETE solution together with its corresponding illustration. Encircle your final answer. 1. A prism has a square base with edges measuring 8 inches each. Find the height, lateral area, and surface area and of the prism if its volume is 768 cubic inches.

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2. A fish tank in the form of a rectangular prism has the following dimensions 60 centimeters by 15 centimeters by 34 centimeters is 1 / 3 full of water. How much water is needed to fill the tank completely?

3. If you could only have one person per 15 m3 to meet fire safety standards, how many people could stay in this ski chalet?

4. Irma enjoyed visiting the Manila Zoo and was so fascinated by the reptile exhibit. Not being able to visit the zoo due to the pandemic she got her very own pet lizard. Irma bought a terrarium shaped like a rectangular prism for her lizard to live in. The terrarium is 20 inches long, 15 inches wide, and 12 inches tall. What is the volume of the terrarium?

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A. Definition A cylinder is a solid figure with two flat circular bases, connected by a curved surface. B. Properties of a Cylinder 1) Bases of a cylinder are equal; 2) The altitude of a cylinder is the perpendicular distance between the bases; and 3) Every cross section of a cylinder parallel to the base has an area equal to that of the bases. C. Formulas in Calculating the Surface Area, Lateral Area and Volume of a Cylinder

Surface Area

SA = LA + 2B SA=𝟐𝝅𝒓𝒉 + 𝟐𝝅𝒓𝟐

Volume Lateral Area

LA = 𝟐𝝅𝒓𝒉

V = Bh V =𝝅𝒓𝟐 𝒉

MATH CHECKPOINT! Complete the table below by solving the missing values. Use the formula in computing or calculating the surface area, lateral area, and volume of a cylinder. Keep your paper clean and organized. (Total: 15 points) Radius of Base (r)

Height of the Cylinder (h)

1) 10 cm

20 cm

2) 6 in

14 in

3)

25 ft

4)

6 dm

5) 4 in

Surface Area (SA)

Lateral Area (LA)

Volume (V)

471.2389 ft2 or 𝟏𝟓𝟎𝝅 923.6282 ft3 or 𝟐𝟗𝟒𝝅 301.5929 ft2 or 𝟗𝟔𝝅

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D. Word Problems Involving Cylinder Read and analyze each item below, then solve what is being asked. Show your COMPLETE solution together with its corresponding illustration. Encircle your final answer. 1. A certain company manufactures tin cans. It received an order for 11,000 cylindrical tin cans of height 6 in. and diameter 5 in. How many square feet of tin did this order require if only 6 square inches is allowed for waste and seams in each can?

2. A paint manufacturer desires a cylindrical steel drum to hold 55 gal. of roof paint. For convenience in handling, it is found necessary to limit the inside diameter to 2.5 ft. What is the height of the drum desired? (1 gal=231 cu. in.)

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3. If a lead pipe 0.75 in. thick has an inner diameter of 2.5 in., how many cubic inches of lead in a piece of pipe 13 ft. long?

4. A 1000-gallon oil tank in the form of a right circular cylinder has a height of 4 ft. What is the diameter of the tank? (1 gal=231 cu. in.)

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ASSESSMATH TIME! I.

Problem Solving. Read and analyze each item below, then solve what is being asked. Show your COMPLETE solution together with its corresponding illustration. Encircle your final answer. (5 points per problem; Total: 20 points) 1. A marble column in the shape of a cylinder is 9 m high and 82 cm in diameter. If the mass of 1 m3 of marble is 3 000 kg, what is the mass of the column?

2. Manuel is one of the farmers in BSU. During some parts of the year, the amount of rain in La Trinidad is not sufficient to maintain the maximum growth of crops. Manuel decided to buy a water tank. How much water will the water tank hold if it is a right circular cylinder with a height of 10 feet and a radius of 5 feet?

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3. A soup can has a diameter of 10 cm and a height of 15 cm. What is the volume of the soup in the can if 0.5 cm of space is left at the top of the can to allow for expansion? If the manufacturer wanted to place a label that will cover the lateral area of the can, how many cm2 of paper is needed?

4. A plant box is 8 feet long and 2 feet wide. The container is filled with soil to a height of 3 feet in the planter. What is the volume of soil in the planter?

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5. Antonio wants to grow some tomatoes in four large planters. He wants each planter to have a volume of 320 cubic feet, but he wants them all to be different. Show four different ways Antonio can make these planters, and draw diagrams with the planters' measurements on them.

6. At an ice carving competition, each carver starts with a block of ice with the dimensions 2m by 3m x 4m. The block is wrapped in a special reflective material to keep it from melting before the competition starts. Disregarding the overlapping parts, how much reflective material is needed to cover the ice?

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Math-in-Action! You are a creative designer specializing in making home decor. As the yuletide season is approaching, you wanted to create eco-friendly home decorations. You are going to present your work for evaluation and critiquing before deciding whether it will be mass-produced at the end of the month. You will be presenting your home decors to your superiors to evaluate your work in terms of units and scale, appropriateness of material used, and the presence of solid mensuration concepts. The main performance task will be presented through a video or series of pictures showing the process of how you created the home decor until you came up with the final product. Criteria

Excellent 4

Proficient 3

Developing 2

Beginning 1

Units and Scale (4 points)

All units are described (in a key or with labels) and the scale is appropriately sized.

Most units are described (in a key or with labels) and the scale is appropriately sized.

All units are described (in a key or with labels) but the scale is not appropriately sized.

Units are not described. Scale is not provided.

Presence of Solid Mensuration Concepts (4 points)

All properties of the solid can easily be seen.

Most properties of the solid can easily be seen.

Some of the properties of the solid cannot be seen.

The solid does not show any of its properties.

Most materials used are appropriate and aligned with the goal of helping the environment.

Some materials used are appropriate and aligned with the goal of helping the environment.

None of the materials used is appropriate and are not aligned with the goal of helping the environment.

Appropriateness of Materials Used (2 points)

All materials used are appropriate and aligned with the goal of helping the environment.

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Mini-Task: Draw a draft or layout of your home decor. Make sure to use proper scaling, include the measurements, and on the latter part a short description of your work. Include the following views: 3D, front, top, rear, and sides. (Illustration of different views: 15 points; Explanation: 5 points; Total: 20 points) Layout:

Description: _____________________________________________________________________________________________ _____________________________________________________________________________________________ _____________________________________________________________________________________________ _____________________________________________________________________________________________ _____________________________________________________________________________________________ _____________________________________________________________________________________________ _____________________________________________________________________________________________ _____________________________________________________________________________________________

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MATH TO PONDER!

I enjoyed learning about ___________________________________________________________________ ________________________________________________________________________________________ ________________________________________________________________________________________ I had a problem with ______________________________________________________________________ ________________________________________________________________________________________ ________________________________________________________________________________________ I want to ask my teacher the question/s _______________________________________________________ ________________________________________________________________________________________ ________________________________________________________________________________________

Congratulations! You were able to finish this module. Hopefully you had a great learning experience. Do not forget the lessons you’ve learned for you will be able to use it on the succeeding topics.

Alimondo, Monica S. and Palasi, Florence D. (2014) Course manual in Solid Geometry. Benguet State University, College of Arts and Sciences, Math-Physics-Statistics Department Buasen, Julie A. (2013) Course manual in Plane Geometry. Benguet State University, College of Arts and Sciences, Math-Physics-Statistics Department Dela Peña, Carmen R. & Limjap, Numidas O., Basic Algebra for secondary schools, First Year. Phoenix Publishing House Inc. Quezon City, Philippines Kern, Williams F. and Bland, James R. (1938). Solid Mensuration with proofs. John Wiley & Sons Inc. Marasigan, Jose A, Coronel, Antonio C., & Coronel, Iluminada C., (2003) Elementary Algebra based on the 2002 BEC. The Bookmark Inc. Makati City, Philippines Oronce, Orlando A. and Mendoza, Marilyn O. (2011) Worktext in Mathematics E-math III. Revised Edition. Manila, Philippines Rex Book Store

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