Volume of Prisms and Pyramids. CHAPTER OUTLINE. 1.1. Surface Area from Nets. 1.2. Surface Area of Prism. 1.3. Lateral, Base, Total Surface Area of Pri...

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Michael Fauteux, (MichaelF) Rosamaria Zapata, (RosamariaZ) CK12 Editor

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AUTHORS Michael Fauteux, (MichaelF) Rosamaria Zapata, (RosamariaZ) CK12 Editor

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Chapter 1. Unit 7, Surface Area and Volume of Prisms and Pyramids

C HAPTER

1

Unit 7, Surface Area and Volume of Prisms and Pyramids

C HAPTER O UTLINE 1.1

Surface Area from Nets

1.2

Surface Area of Prism

1.3

Lateral, Base, Total Surface Area of Prisms

1.4

Lateral, Base, Total Surface Area of Pyramids

1.5

Volume of Prisms

1.6

Volume of Pyramids

1.7

Quiz for Lessons 1-6

1.8

Change of Dimension

1.9

Unit 7 Exam

1.10

Unit 7 Exam Key

1

1.1. Surface Area from Nets

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1.1 Surface Area from Nets

Lesson Plan Launch (10 min) • Students: Students find the composite area of a shape. Presentation (20 min) • (15 min) Use the extension questions to jump into definition of surface area. (Discussion) – Definition: total Area of the surface of a three-dimensional solid. – Definition PRISM: A three-dimensional object with parallel, congruent bases * Emphasize definition by having students sketch a picture. (Sketch 2 congruent triangle then connect all bases) – Definition PYRAMID: A three-dimensional solid with a polygon base and triangular sides all connecting at the Apex. * Emphasize definition by having students sketch a picture. • (5 min) Explain directions to practice and hand out rulers. Practice (15 min) • Students use composite area to find area of nets and ultimately surface area. Conclusion (10 min) • Students explain in complete sentences the difference between the surface area of a square prism and the area of a square. Exit Ticket (5 min) Materials • Lesson packets • Exit Tickets

Launch Find the area of the composite shape below. Please organize your work and show all your work to the right of the shape. 2

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Chapter 1. Unit 7, Surface Area and Volume of Prisms and Pyramids

Extension: It is your best friend’s birthday and you bought them a gift that would fit in the box below. How much wrapping paper would you need to wrap it?

Presentation What is surface Area?

Practice

3

1.1. Surface Area from Nets

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Instructions: Find the total surface area of the 3-dimmensional objects by breaking it down into pieces. Be sure to show all your work and provide a clear solution Rectangular Prism Total Surface Area: Similar Real World Object: Square Pyramid Total Surface Area: Similar Real World Object:

Triangular Pyramid Total Surface Area: Similar Real World Object: Trapezoidal Prism Total Surface Area: Similar Real World Object: Challenge: On a separate sheet of paper, sketch the net for a Pentagonal Prism. Then, find the surface area of the net your created.

Conclusion What is the difference between the surface area of a square prism (3-dimmentional) and the area of a square (2Dimmensional)? Try to use at least three sentences and 3 words 4

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Chapter 1. Unit 7, Surface Area and Volume of Prisms and Pyramids

Sides Surface Area

Composite

Shape

Polygon

2−D

Area 3−D

Homework 1. Find the surface area of the net below.

Total Surface Area: 2. Explain the difference between a prism and a pyramid. _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ 3. Explain: What does a net have to do with the surface area of a 3-D object? _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ 5

1.1. Surface Area from Nets _________________________________________________________

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Chapter 1. Unit 7, Surface Area and Volume of Prisms and Pyramids

1.2 Surface Area of Prism

Lesson Plan Launch (10 min) • Students: Prior knowledge we will need today: – Name the shape, write the area formula, create heights of different shapes – Define prism Presentation (25 min) • (5 min) Explain directions to practice and hand out rulers. • (10 min) Task: Class split into 5-6 groups → Groups measure rectangular prism and find surface area – Solution must include pictures, relevant formulas, organization, proper units – Groups present their work on chart paper (stick on board with brief presentation) • (10 min) Can we do the same thing from a picture of a prism? – Teacher: demo pulling apart. * Before class, get a shoe box and put paper that represents the area of each side. Label each side front, back, left, right, top, bottom. Pull sticky sections off each side of demo box prism, stick to board, name: front, back, left, right, top, bottom) – Organization: verbal model; picture model; Algebraic model (tell the whole story!) * Verbal model: Front Rect. + Back Rect + Top Rect + Bottom Rect + Left Rect + right Rec * Picture model: Picture of dimensions of each side * Algebraic: Find the area of each individual piece and add together. Practice (15 min) • Students calculate the surface area of various prisms using verbal, pictorial and Algebraic models • Emphasize the pictorial and Algebraic (formulas) Conclusion (10 min) • Students create their own prism based on a given surface area. Exit Ticket (5 min) Materials • • • • •

Lesson packets Exit Tickets Boxes (6) – Preferable 3 pairs so groups can compare Rulers Chart paper 7

1.2. Surface Area of Prism

Launch 1) Name the shape and give its area formula. a. Name:

A= b. Name:

A= c. Name:

A= d. Name:

A= e. Name: 8

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Chapter 1. Unit 7, Surface Area and Volume of Prisms and Pyramids

A= f. Name:

A= 2) Sketch the height given the base of the shape. a.

b.

c.

9

1.2. Surface Area of Prism

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3) Fill in the blanks with one of the following words: 3-D Congruent Rectangle Parallel Solid A prism is a ___________ ___________ with ___________ and ___________ bases and ___________ 4) Surface area is ______________________________________________ _________________________________________________________ _________________________________________________________

Presentation Taking apart the picture: Can we find the surface area of a prism from a given picture?

Practice PROFICIENT Instructions: Find the total surface area of the prisms below by breaking it down like we did above. Write out verbal, picture, and algebraic models for each example. Be sure to use correct units and be clear with your solution 1.

2. 10

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Chapter 1. Unit 7, Surface Area and Volume of Prisms and Pyramids

3.

ADVANCED 4.

5.

6. 11

1.2. Surface Area of Prism

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Conclusion Create a prism with a total surface area of 72 cm2 . Sketch the prism, Label its dimensions, and show how you know the surface area is 72 cm2

Homework Find the surface area for the questions below. 1.

2.

3.

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Chapter 1. Unit 7, Surface Area and Volume of Prisms and Pyramids

4. A gift box measures 40 in. by 28 in. by 12 in. Can the box be completely covered by a 30 − f t 2 roll of wrapping paper? Why or why not? Hint: watch your units!

Exit Ticket

13

1.3. Lateral, Base, Total Surface Area of Prisms

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1.3 Lateral, Base, Total Surface Area of Prisms

Lesson Plan Launch (10 min) • Students: Shade the base of a rectangular/ triangular prism – In a prism, there has to be two CONGRUENT, PARALLEL polygons to have it be the base. • Students come up with a definition of “lateral” from descriptions – Have the students touch their “lats” for kinesthetic learners. Presentation (25 min) • (10 min) Sketch a REGULAR HEXAGONAL PRISM (two congruent hexagons with rectangular sides) – Define Base Area: the area of only one the bases – Define Lateral Area: Sum of the 6 rectangular sides * There is the same number of lateral pieces as the number of sides of the base. * Refer to as the “walls” of the shape. – Define total surface area: the sum of both bases and the 6 congruent sides * The base has 6 sides, how many “sides” are there? * The sides are called “lateral faces” (label pic) • (15 min) Work through the 2 examples on the next page – Emphasize “shade the base” – There is the same number of lateral pieces as the number of sides of the base. Practice (15 min) • Students find Lateral, base, and total area of different shapes. Conclusion (10 min) • Sketch a prism with a surface area of 24 units squared – If time, have them trade with a neighbor and check their work OR find lateral area. Exit Ticket (5 min) Materials • Lesson packets • Exit Tickets 14

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Chapter 1. Unit 7, Surface Area and Volume of Prisms and Pyramids

Launch 1. Shade the base of the rectangular prism.

2. Shade the base of the triangular prism.

3. On a map, the longitudelatitude is the line that runs east to west. In football, the quarterback may throw a lateral If you work out a lot, you may see a machine that works out your “lats What do you think “lateral” means? Where else have you heard a word similar to lateral? _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ 15

1.3. Lateral, Base, Total Surface Area of Prisms

Presentation B = Base Area :

LA = Lateral Area :

SA = Total Surface Area :

1. Find the base, lateral, and total surface area of the triangular prism below.

2. Find the base area, lateral area, and total area of the isosceles trapezoidal prism below.

Practice 1. Find the base, lateral, and total surface area of the rectangular prism below. (the base is shaded) 16

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Chapter 1. Unit 7, Surface Area and Volume of Prisms and Pyramids

2. Find the base, lateral, and total surface area of the triangular prism below.

3. Find the base, lateral, and total surface area of the isosceles trapezoidal prism below.

4. Find the base, lateral area, and total surface area of the regular hexagonal prism below.

5. Find the lateral area of the triangular prism below.

17

1.3. Lateral, Base, Total Surface Area of Prisms 6. Find the lateral area of the isosceles trapezoidal prism below.

Conclusion Sketch the lateral faces, with their dimensions, of the prisms below. 1.

2.

Homework 1. Find the base and lateral area of the rectangular prism below (the base is shaded).

2. Find the lateral and total surface area of the triangular prism below. 18

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Chapter 1. Unit 7, Surface Area and Volume of Prisms and Pyramids

Exit Ticket

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1.3. Lateral, Base, Total Surface Area of Prisms

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Chapter 1. Unit 7, Surface Area and Volume of Prisms and Pyramids

1.4 Lateral, Base, Total Surface Area of Pyramids

Lesson Plan Launch (10 min) • Students: break down the pyramids into their shapes for base, lateral, and surface areas. Also students take guesses and label the parts of a pyramid. Encourage the students to EDUCATED GUESSES – In a pyramid, is only ONE base with triangular sides that meet at the APEX Presentation (30 min) • (5 min) Debrief # 4 from the launch completely. Make sure to define any words that you feel the students need defined. But “Shade the base and bold the height” (Of the entire shape). Compare this to the slant height and the fact that they are two different heights. Very confusing for students. • (10 min) Relate a 3-D model to a net of a pyramid – Have students sketch the net. Have students even shade the base. This will help students see how to break it down and find base area and lateral area by sketching the net. – This method will also help students not miss a piece. Most common mistake for finding Lateral or surface area is missing a lateral piece. • (15 min) Work through the 2 examples on the next page – Focus on clear solutions. • Point out that the shape of the base always exists in the instructions. i.e. Square base. Practice (15 min) • Students find Lateral, base, and total area of different shapes. Conclusion (10 min) • Real world application of lateral area of a pyramid. – This is a multistep problem. Encourage students to “Size up the problem” before jumping in. Exit Ticket (5 min) Materials • Lesson packets • Exit Tickets • Nets of Pyramids (For remediation for some students) 21

1.4. Lateral, Base, Total Surface Area of Pyramids

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Launch

1. What is the shape of the BASE in the pyramid on the left? Sketch it here. 2. What is the shape of the LATERAL pieces on the pyramid on the left? How many are there? Sketch them here. 3. How does the number of LATERAL pieces relate to the number of sides of the BASE?

4. Label the square pyramid below with the following vocabulary words. Make Guesses!!! a) Base edge b) Lateral edge c) Slant height d) Pyramid height e) Apex

Presentation Square Pyramid 22

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Chapter 1. Unit 7, Surface Area and Volume of Prisms and Pyramids

Net of a Pyramid 1. Find the base area, lateral area, and total area of the square pyramid below.

2. Find the base area, lateral area, and total area of the equilateral triangular pyramid below.

23

1.4. Lateral, Base, Total Surface Area of Pyramids

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Practice 1. Find the base area, lateral area, and total area of the square pyramid below.

2. The base edge of the shape below is 12 cm and the slant height is 10 cm. Find the base area, lateral area, and total area of the equilateral triangular pyramid below.

3. Find the base area, lateral area, and total area of the regular hexagonal pyramid below. 24

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Chapter 1. Unit 7, Surface Area and Volume of Prisms and Pyramids

Conclusion The Pyramid of Giza (a square pyramid in Egypt) is one of the 7 wonders of the world. The pyramid is 480 feet high and the slant height is 610 ft. How many square feet of gold would you need to cover the pyramid? If gold costs $120 per square foot, what would be the cost of covering the whole pyramid?

Homework

1. Name the 3-D solid _________________________________________________________ 2. Sketch the net of the shape below. 3. Find the base area (provide a clear solution). 4. Find the lateral area (provide a clear solution). 5. The Luxor hotel and Casino in Las Vegas is a pyramid shaped hotel that is completely made of glass. If the owner wanted to replace ALL the windows in the hotel, would he need to figure out the: base area, lateral area, or surface area? Why? _________________________________________________________ _________________________________________________________ 25

1.4. Lateral, Base, Total Surface Area of Pyramids _________________________________________________________ _________________________________________________________ _________________________________________________________

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Chapter 1. Unit 7, Surface Area and Volume of Prisms and Pyramids

1.5 Volume of Prisms

Lesson Plan Launch (10 min) • Students: Relate surface area and volume to parts of different objects. – Debrief: Pair/ Share Presentation (30 min) • (10 min) Teacher lead investigation – Hand out 6 snap cubes out to as many students as you can. Let them “play” – Instruct them to assemble 2 rows of 3 * What is the surface area? Volume? Why? – Find a friend and stack them. Now what is the volume? – Again. . . until emphasizing point that it’s just adding another row of the base on top – Conjecture: How do we find volume of a prism? – Make a funky shape with 6 cubes repeat process. Always hold true? • (5 min) Debrief by letting them complete the sentence starter on the bottom of the launch. Share out a couple then find the volume of the rubix cube. – Relate volume of a prism to how many hotel rooms are in a hotel. * “How many hotel rooms are in the first floor? How many rooms are in the entire building?” • (10 min) Work through examples. – Encourage students to shade the base and bold the height. Practice (15 min) • Students use the menu to choose their problems. Complete any 6. Conclusion (10 min) • How would we find how much water we would need to fill the pool? Discuss. Exit Ticket (5 min) Materials • Lesson packets • Exit Tickets • Snap cubes (about 200) premade in groups of 6. – If you don’t have a class set, have at least 10 for yourself to model for the class. 27

1.5. Volume of Prisms

Launch 1. Sketch an example of a: Birthday Present What would represent surface area of a birthday present? _________________________________________________________ _________________________________________________________ What would represent volume of a birthday present? _________________________________________________________ _________________________________________________________ 2. Sketch an example of a: Soccer Ball What would represent surface area of a Soccer Ball? _________________________________________________________ _________________________________________________________ What would represent volume of a Soccer Ball? _________________________________________________________ _________________________________________________________ 3. Sketch an example of a: stuffed animal What would represent surface area of a stuffed animal? _________________________________________________________ _________________________________________________________ What would represent volume of a stuffed animal? _________________________________________________________ _________________________________________________________

Presentation

Surface area is ________________________________________ 28

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Chapter 1. Unit 7, Surface Area and Volume of Prisms and Pyramids

Volume is ______________________________________________ Determine whether you need to measure surface area or volume in the situations below. 1. The cushions of an old sofa need to be re-stuffed. Surface area / Volume why? 2. The old sofa is out of style and needs to be reupholstered Surface area / Volume why? 3. A manufacturer of paper bags must determine the cost of the paper to make the bags. Surface area / Volume why? 1. Find the volume of the triangular prism.

2. Find the volume of the trapezoidal prism.

Practice Menu of options: Choose a minimum of 6 problems. Challenge yourself!!! 29

1.5. Volume of Prisms

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Conclusion The base of a rectangular swimming pool is sloped so one end of the pool is 6ft deep and the shallow end is 3ft deep. If the length of the pool is 20ft and the width of the pool is 15ft, 30

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Chapter 1. Unit 7, Surface Area and Volume of Prisms and Pyramids

How might you find the volume of the water that it would take to fill the pool? ________________________________________________________ ________________________________________________________ ________________________________________________________ ________________________________________________________

Homework 1. Find the volume of the trapezoidal prism below.

2. Sketch a rectangular prism that is 8 cm long, 11 cm wide and 18 cm high. Find the volume. 3. a. Sketch a box with a surface area of 60 in2 . b. Sketch a box with a volume of 60 in3 . c. Which box is bigger? Explain your answer. _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ 4. Find the volume of the net below. 31

1.5. Volume of Prisms

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Chapter 1. Unit 7, Surface Area and Volume of Prisms and Pyramids

33

1.6. Volume of Pyramids

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1.6 Volume of Pyramids

Lesson Plan Launch (10 min) • Students: Calculate the volume of a square prism. Then, how does the volume of a pyramid relate to the volume of a prism? – Encourage students to take an educated guess. – Students Pair/ Share and Report Out. Presentation (25 min) • (10 min) Teacher lead investigation – Arrange the desks so all students can see a demonstration. For example, in a circle. – Teacher guides students through the information about the prism solid. Find the measure (using a ruler) of base edges and the height. Fill out graphic organizer on prism. – Teacher guides students through the information about the pyramid (base and height). Let students know that the objective of the investigation is to compare and contrast the formula of volume of a prism and volume of a pyramid. – Ask students to answer the first two questions in the third column. Debrief quickly. – Teacher (or a student who will model the whole investigation) fills up the pyramid solid with rice and asks the class: How many of these will it take to fill up the Prism? Have students make the prediction on their paper. Have students report out predictions and record on the board. – Complete the demonstration by pouring the rice from the pyramid into the prism. How many did it take to fill it up? (3) So the pyramid is (one third) the volume of the prism. Might have to start with “the volume of the prism is 3 times the volume of the pyramid” – Write formula for volume of a pyramid and quickly answer the problem below. • (10 min) Examples: Work through examples on next page. Be sure to clarify any common mistakes. Practice (15 min) • Students use the menu to choose their problems. Complete any 6. Conclusion (10 min) • Find the weight of a pyramid. Hand out calculators to help complete conclusion Exit Ticket (5 min) Materials 34

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Chapter 1. Unit 7, Surface Area and Volume of Prisms and Pyramids

Lesson packets Exit Tickets Hollow prism and pyramid models with congruent bases Rice Ruler

Launch 1. Find the volume of the square prism.

2. Notice that the base of the prism and the pyramid are the same. Notice that the height of the prism and the pyramid are the same as well. Prediction: Do you believe that the volume of the pyramid with the same base area and same height will be the same as the prism? Half the volume? Less than half the volume? More than half? Complete this sentence: I think the volume of the pyramid is. ________________________________ ________________________________ ________________________________

Presentation TABLE 1.1: Compare/Contrast Prism B= h= Volume:

Pyramid B= h= Volume:

Investigation Are the bases the same area? ___________ 35

1.6. Volume of Pyramids Are the heights the same? ______________ Predict: How may pyramids of rice will it take to fill up the prism? _____________________________________ Results: The volume of a pyramid is _____________________________________ 1. Find the volume of the square pyramid:

2. Find the volume of the square pyramid.

3. Find the volume of the square pyramid. 36

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Chapter 1. Unit 7, Surface Area and Volume of Prisms and Pyramids

Practice

Menu of options: Choose a minimum of 6 problems. Challenge yourself!!!

37

1.6. Volume of Pyramids

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Conclusion The Great Pyramid of Giza is a square pyramid with base edges of approximately 775 ft and an original pyramid height of 480 ft. The limestone used to construct the pyramid weights approximately 167 pounds per cubic foot. How much does the pyramid weigh? If 1 ton = 2000 pounds, how many tons does it weigh?

Homework 1. Find the volume of the square pyramid. 38

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Chapter 1. Unit 7, Surface Area and Volume of Prisms and Pyramids

2. Sketch a rectangular pyramid with a base of 8 cm by 11 cm. The height of the pyramid is 20 cm. Find the volume. 3. Find the volume of the square pyramid.

4. Find the volume of the square pyramid.

39

1.6. Volume of Pyramids

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Chapter 1. Unit 7, Surface Area and Volume of Prisms and Pyramids

1.7 Quiz for Lessons 1-6 Name: _________________________ Instructions: Be sure to include clear solutions with all work. Also, box your answer and include correct units.

1. Find the total surface area of the triangular prism 2. Find the volume of the triangular prism.

3. Find the lateral area of the square pyramid. 4. Find the total surface area of the square pyramid 5. Find the volume of the square pyramid.

41

1.8. Change of Dimension

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1.8 Change of Dimension

Lesson Plan Launch (20 min) • Quiz: lessons 1-5 Presentation (20 min) • (15 min) Teacher lead investigation – Choose 3 students to come to the board and solve for the surface area of each prism. * How do the dimensions compare to #1? (double, triple etc) * What do you notice? What are your observations about how the surface areas compare to #1? * Summarize findings of discussion. – Choose 3 new students to come to the board and solve for the volume of each prism. * How do the dimensions compare to #1? * What do you notice? What are your observations about how the volumes compare to #1? * Summarize findings of discussion. • (5 min) Discuss the following example problems – Talk about how we could solve without numbers * Students need to experiment. Encourage them to make their own examples to look for a pattern or answer. Practice (15 min) • Students complete practice problems. • Have them experiment by making up their own problems. Conclusion (10 min) • Find the weight of a pyramid. Hand out calculators to help complete conclusion Exit Ticket (5 min) Materials • Lesson packets • Exit Tickets • Quiz lesson 1-6 42

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Chapter 1. Unit 7, Surface Area and Volume of Prisms and Pyramids

Presentation

Practice ∗∗The best way to solve these problems is by experimenting∗∗ 1) The length of each side of a cube is multiplied by 3. What is the change in surface area A. The surface area is 3 times greater. B. The surface area is 6 times greater. C. The surface area is 9 times greater. D. The surface area is 27 times greater. 2) The length of each side of a cube is multiplied by 3. What is the change in volume A. The volume is 3 times greater. B. The volume is 6 times greater. C. The volume is 9 times greater. 43

1.8. Change of Dimension

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D. The volume is 27 times greater. 3) The lateral edge and height of a cube are each divided by 4. What is the change in surface area A. The surface area is B. The surface area is C. The surface area is

1 16 of the original. 1 4 of the original. 1 64 of the original.

D. The surface area is 4 of the original. 4) A Square Prism has a base edge of 4 ft and a height of 10 ft. Suppose you can either double the base edgedouble the height. Which change will create a greater surface area? A. Doubling the lateral. B. Doubling the height. C. They result in the same surface area. D. Not enough information to determine. 5) A pyramid has a height of 10 ft and a square base with edge length 7 ft. How does the volume change if the base stays the same and the height is doubled? How does the volume change if the height stays the same and the edge length is doubled? Explain why your answers are true for any height and any edge length.

Conclusion Choose one pair of key terms below. Explain how they are similar and how they are different Height/slant height Base area/lateral area Surface area/volume Area/surface area Use the word bank to help you explain your answer in 3-4 complete sentences.

Homework A cereal company fills their honey-oats cereal boxes with 160 cm2 of cereal. a. Design at least 2 different boxes that would hold the cereal. 44

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Chapter 1. Unit 7, Surface Area and Volume of Prisms and Pyramids

b. Which of your designs uses the least amount of material?

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1.9. Unit 7 Exam

1.9 Unit 7 Exam Name: _________________________ Date: _________________________ 1. What is the name of the three dimensional solid?

a. b. c. d.

Square Prism Square Pyramid Rectangular Prism Rectangular Pyramid

2. What is the area of one base in the right triangular prism?

a. b. c. d.

6 in2 8 in2 24 in2 30 in2

3. What is the shape of a lateral face of a pyramid? a. b. c. d.

Triangle Square Rectangle Apex

4. What is the height of the pyramid below?

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Chapter 1. Unit 7, Surface Area and Volume of Prisms and Pyramids

6 ft 8√ ft 3√ 5 f t 117 f t

5. A hexagonal prism has a height of 20 inches and a base area of 6 square inches. What is the volume of the prism? a. b. c. d.

100 in3 120 in3 720 in3 26 in3

6. True/ False: The pyramid height is not visible on its net. a. True b. False 7. The roof of a house is a square pyramid with a base edge of 10 feet and the slant height is 7 feet.

What is the lateral area of the roof? a. b. c. d.

35 f t 2 70 f t 2 140 f t 2 240 f t 2

8. The four sides of this figure will be folded up and be taped to make an open box.

What is the volume of the prism? a. b. c. d.

50 un3 75 un3 100 un3 125 un3

9. Which net would build a pyramid with a surface area of 24 un2 ? 47

1.9. Unit 7 Exam

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a.

b.

c.

d. 10. All the edges of a cube are multiplied by 4. What is the change in the surface area of the cube? a. b. c. d. 48

The surface area is 4 times greater. The surface area is 8 times greater. The surface area is 16 times greater. The surface area is 24 times greater.

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Chapter 1. Unit 7, Surface Area and Volume of Prisms and Pyramids

11. A square prism has a base edge of 2 feet and a height of 5 feet. If you double all the edges, how will that effect the volume? a. b. c. d.

The volume is 2 times greater. The volume is 5 times greater. The volume is 6 times greater. The volume is 8 times greater.

Free Response Section – Be sure to include a clear solution with all your work. If there is no evidence for an answer you will not receive credit. Also, box your answer and include correct units for full credit.

1. Find the total surface area of the rectangular prism. 2. Find the volume of the rectangular prism.

3. Find the lateral area of the triangular prism. 4. Find the volume of the triangular prism.

5. Find the total surface area of the isosceles trapezoidal prism. 6. Find the volume of the prism. 49

1.9. Unit 7 Exam

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7. The pyramid to the left is labeled with letters instead of numbers. Assign the letters with the correct vocabulary word below. Each letter can only be used once. Base Edge: __________ Lateral Edge: __________ Slant Height: __________ Pyramid Height: __________ Apex: __________

8. Explain, using 3-4 complete sentences, how you would find the lateral area of the square pyramid. ________________________________________________________ ________________________________________________________ ________________________________________________________ ________________________________________________________ ________________________________________________________ ________________________________________________________ ________________________________________________________ 9. Find the lateral area of the square pyramid. 10. Find the volume of the pyramid.

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Chapter 1. Unit 7, Surface Area and Volume of Prisms and Pyramids

1.10 Unit 7 Exam Key Name: _________________________ Date: ________________ 1. 2. 3. 4. 5. 6. 7. 8. 9.

(c) Rectangular Prism (a) 6 in2 (a) Triangle √ (c) 3 5 f t (b) 120 in3 (a) True (c) 140 f t 2 (a) 50 un3 (b)

10. (c) The surface area is 16 times greater. 11. (d) The volume is 8 times greater. Free Response Section – Be sure to include a clear solution with all your work. If there is no evidence for an answer you will not receive credit. Also, box your answer and include correct units for full credit. 1. SA = 2(72) + 2(54) + 2(108) = 468 in2 3 points distributed at teachers discretion. 2. V = Bh height depends on base = (72)9 = (54)12 = (108)6 = 648 in3 3. √ LA = 24 2 + 24 + 24 √ = 48 + 24 2 cm2 3 points distributed at teachers discretion. 51

1.10. Unit 7 Exam Key

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4. V = Bh 9 = 8 = 36 cm3 2 5. 4 SA = 2 (5 + 12) + 2(30) + 5(6) + 12(6) 2 = 68 + 60 + 30 + 72 = 230 f t 2 6. V = Bh = (34)6 = 204 f t 3 7. Base Edge: G Lateral Edge: H Slant Height: R Pyramid Height: F Apex: S 8. Explain, using 3-4 complete sentences, how you would find the lateral area of the square pyramid. _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ 9.

6(5) LA = 4 2 = 4(15) = 60 m2 10. 1 Bh 3 1 = (36)4 3 = 48 m3

V=

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