# Pre-Algebra Interactive Chalkboard Copyright by The McGraw-Hill Companies, Inc. Send all inquiries to:

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Pre-Algebra Interactive Chalkboard Copyright by The McGraw-Hill Companies, Inc. Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240

2

3 Click the mouse button or press the Space Bar to display the answers.

4 Lesson 11-1Three-Dimensional Figures Lesson 11-2Volume: Prisms and Cylinders Lesson 11-3Volume: Pyramids and Cones Lesson 11-4Surface Area: Prisms and Cylinders Lesson 11-5Surface Area: Pyramids and Cones Lesson 11-6Similar Solids Lesson 11-7Precision and Significant Digits

5 Example 1 Identify Prisms and Pyramids Example 2 Identify Diagonals and Skew Lines Example 3 Analyze Real-World Drawings

6 Identify the solid. Name the bases, faces, edges, and vertices. Answer: This figure has two parallel congruent bases that are rectangles, GHJK and LMNP, so it is a rectangular pyramid. faces: GHJK, LMNP, GHML, HJNM, JKPN, GKPL edges: vertices: G, H, J, K, L, M, N, P

7 Identify the solid. Name the bases, faces, edges, and vertices. Answer: This figure has one triangular base, DEF, so it is a triangular pyramid. faces: DEF, DEG, DFG, EFG edges: vertices: D, E, F, G

8 Identify each solid. Name the bases, faces, edges, and vertices. a. Answer: rectangular pyramid base: BCDE faces: ABC, ACD, ADE, AEB, BCDE edges: vertices: A, B, C, D, E

9 Identify each solid. Name the bases, faces, edges, and vertices. b. Answer: rectangular prism bases: GHJK, LMNP or GKPL, HJNM or GHML, KJNP faces: GHJK, LMNP, GHML, HJNM, JKPN, GKPL edges: vertices: G, H, J, K, L, M, N, P

10 Identify a diagonal and name all segments that are skew to it. Answer: is a diagonal because vertex Q and vertex W do not intersect any of the same faces;

11 Identify a diagonal and name all segments that are skew to it. Answer:

12 Architecture An architect s sketch shows the plans for a new office building.

13 Find the area of the ground floor if each unit on the drawing represents 55 feet. The drawing is 6 5, so the actual dimensions are 6(55) 5(55) or 330 feet by 275 feet. Formula for area Answer: The area of the ground floor is 90,750 square feet.

14 How many floors are in the office building if each floor is 12 feet high? Assume each unit on the drawing represents 40 feet. You can see from the side view that the height of the building is 3 units. total height: number of floors: Answer: There are 10 floors in the office building.

15 Architecture An architect s sketch shows the plans for a new office building.

16 a. Find the area of the ground floor if each unit represents 75 feet. Answer: 168,750 ft 2 b. How many floors are in the office building if each floor is 15 feet high? Assume each unit on the drawing represents 45 feet. Answer: 9 floors

17

18 Click the mouse button or press the Space Bar to display the answers.

19 Example 1 Volume of a Rectangular Prism Example 2 Volume of a Triangular Prism Example 3 Height of a Prism Example 4 Volume of a Complex Solid Example 5 Volume of a Cylinder

20 Find the volume of the prism. Formula for volume of a prism The base is a rectangle, so Simplify. Answer: The volume is 3200 cubic centimeters.

21 Find the volume of the prism. Answer: The volume is 45 ft 3.

22 Find the volume of the triangular prism. Formula for volume of a prism B = area of base or. The height of the prism is 3 in.

23 Simplify. Answer: The volume is 15 cubic inches.

24 Find the volume of the triangular prism. Answer: The volume is 15 ft 3.

25 Baking Cake batter is poured into a pan that is a rectangular prism whose base is an 8-inch square. If the cake batter occupies 192 cubic inches, what will be the height of the batter? Formula for volume of a prism Formula for volume of a rectangular prism Simplify. Divide each side by 64. Answer: The height of the batter is 3 inches.

26 Swimming Pool A swimming pool is filled with 960 cubic feet of water. The pool is a rectangular prism 20 feet long and 12 feet wide and is the same depth throughout. Find the depth of the water. Answer: The water is 4 feet deep.

27 Multiple-Choice Test Item Find the volume of the solid. A 262 m 3 B 918 m 3 C 972 m 3 D 1458 m 3 Read the Test Item The solid is made up of a rectangular prism and a triangular prism. The volume of the solid is the sum of both volumes.

28 Solve the Test Item Step 1 The volume of the rectangular prism is 12(9)(9) or 972 m 3. Step 2 In the triangular prism, the area of the base is volume is and the height is 12. Therefore, the Step 3 Add the volumes. Answer: The answer is D.

29 Multiple-Choice Test Item Find the volume of the solid. A 932 in 3 B 896 in 3 C 1432 in 3 D 718 in 3 Answer: The answer is B.

30 Find the volume of the cylinder. Round to the nearest tenth. Formula for volume of a cylinder Replace r with 7 and h with 14. Simplify. Answer: The volume is about cubic feet.

31 Find the volume of the cylinder. Round to the nearest tenth. diameter of base 10 m, height 2 m Since the diameter is 10 m, the radius is 5 m. Formula for volume of a cylinder Replace r with 5 and h with 2. Simplify. Answer: The volume is about cubic meters.

32 Find the volume of each cylinder. Round to the nearest tenth. a. Answer: in 3 b. diameter of base 8 cm, height 6 cm Answer: cm 3

33

34 Click the mouse button or press the Space Bar to display the answers.

35 Example 1 Volumes of Pyramids Example 2 Volume of a Cone Example 3 Use Volume to Solve Problems

36 Find the volume of the pyramid. If necessary, round to the nearest tenth. Formula for volume of a pyramid The base is a square, so The height of the pyramid is 12 inches. Simplify. Answer: The volume is 900 cubic inches.

37 Find the volume of the pyramid. If necessary, round to the nearest tenth. base area 19 cm 2, height 21 cm Formula for volume of a pyramid Replace B with 19 and h with 21. Simplify. Answer: The volume is 133 cubic centimeters.

38 Find the volume of each pyramid. If necessary, round to the nearest tenth. a. Answer: 112 in 3 b. base area 32 cm 2, height 9 cm Answer: 96 cm 3

39 Find the volume of the cone. Round to the nearest tenth. Formula for volume of a cone Replace r with 5.5 and h with 8. Simplify. Answer: The volume is about cubic meters.

40 Find the volume of the cone. Round to the nearest tenth. Answer: in 3

41 Landscaping When mulch was dumped from a truck, it formed a cone-shaped mound with a diameter of 15 feet and a height of 8 feet. What is the volume of the mulch? Formula for volume of a cone Since d = 15, replace r with 7.5. Replace h with 8. Answer: The volume of the mulch is about 471 cubic feet.

42 Landscaping When mulch was dumped from a truck, it formed a cone-shaped mound with a diameter of 15 feet and a height of 8 feet. How many square feet can be covered with this mulch if 1 cubic foot covers 4 square feet of ground? Answer: 1884 square feet can be covered with this mulch.

43 Playground A load of wood chips for a playground was dumped and formed a cone-shaped mound with a diameter of 10 feet and a height of 6 feet. a. What is the volume of the wood chips? Answer: about 157 ft 3 b. How many square feet of the playground can be covered with wood chips if 1 cubic foot of wood chips can cover 3 square feet of the playground? Answer: 471 ft 2

44

45 Click the mouse button or press the Space Bar to display the answers.

46 Example 1 Surface Area of a Rectangular Prism Example 2 Surface Area of a Triangular Prism Example 3 Surface Area of a Cylinder Example 4 Compare Surface Areas

47 Find the surface area of the rectangular prism. Write the formula. Substitution Simplify. Answer: The surface area of the rectangular prism is 1868 square centimeters.

48 Find the surface area of the rectangular prism. Answer: 444 in 2

49 Find the surface area of the triangular prism. Find the area of each face. Bottom Left side Right side Two bases

50 Add to find the total surface area. Answer: The surface area of the triangular prism is 336 square meters.

51 Find the surface area of the triangular prism. Answer: 96 ft 2

52 Find the surface area of the cylinder. Round to the nearest tenth. Formula for surface area of a cylinder Replace r with 2.5 and h with 8. Simplify. Answer: The surface area of the cylinder is about square meters.

53 Find the surface area of the cylinder. Round to the nearest tenth. Answer: in 2

54 Cereals A company packages its cereal in a rectangular prism that is 2.5 inches by 7 inches by 12 inches. It is considering packaging it in a cylindershaped container having a 6-inch diameter and a height of 7.5 inches. Which uses the least amount of packaging? Surface area of rectangular prism top/bottom front/back sides

55 Surface area of cylinder top/bottom curved surface Answer: Since square inches < 263 square inches, the cylinder uses less packaging.

56 Candy A candy company is deciding between two types of packaging for its gumballs. The first option is a rectangular prism that is 6 inches by 4 inches by 1.5 inches. The second option is a cylinder having a radius of 2 inches and a height of 5 inches. Which option requires less packaging? Answer: The rectangular prism requires less packaging. 78 < 88.0

57

58 Click the mouse button or press the Space Bar to display the answers.

59 Example 1 Surface Area of a Pyramid Example 2 Use Surface Area to Solve a Problem Example 3 Surface Area of a Cone

60 Find the surface area of the square pyramid. Find the lateral area and the base area. Area of each lateral face Area of a triangle Replace b with 8 and h with 8.9. Simplify. There are 4 faces, so the lateral area is 4(35.6) or square feet.

61 Area of base Area of a square Replace s with 8 and simplify. The surface area of a pyramid equals the lateral area plus the area of the base. S Answer: The surface area of the square pyramid is square feet.

62 Find the surface area of the square pyramid. Answer: 42 m 2

63 Canopies A canopy is in the shape of a square pyramid that is 3.4 meters on each side. The slant height is 2 meters. How much canvas is used for the canopy? Find the lateral area only, since there is no bottom to the canopy. Area of each lateral face Formula for area of a triangle Replace b with 3.4 and h with 2.

64 Simplify. One lateral face has an area of 3.4 square meters. There are 4 lateral faces, so the lateral area is 4(3.4) or 13.6 square meters. Answer: 13.6 square meters of canvas was used to cover the canopy.

65 Tent A tent is in the shape of a square pyramid that is 8 feet on each side. The slant height is 10 feet. Find the surface area of the tent. Answer: 160 ft 2

66 Find the surface area of the cone. Round to the nearest tenth. Formula for surface area of a cone Replace r with 3.5 and with 10. Simplify. Answer: The surface area of the cone is about square feet.

67 Find the surface area of the cone. Round to the nearest tenth. Answer: cm 2

68

69 Click the mouse button or press the Space Bar to display the answers.

70 Example 1 Identify Similar Solids Example 2 Find Missing Measures Example 3 Use Similar Solids to Solve a Problem

71 Determine whether the pair of solids is similar. Write a proportion comparing radii and heights. Find the cross products. Simplify. Answer: The radii and heights are not proportional, so the cylinders are not similar.

72 Determine whether the pair of solids is similar. Write a proportion comparing corresponding edge lengths. Find the cross products. Simplify. Answer: The corresponding measures are proportional, so the pyramids are similar.

73 Determine whether the pair of solids is similar. a. Answer: yes

74 Determine whether the pair of solids is similar. b. Answer: no

75 The cylinders to the right are similar. Find the radius of cylinder A. Substitute the known values.

76 Find the cross products. Simplify. Divide each side by 6. Answer: The radius of cylinder A is 6 centimeters.

77 The rectangular prisms below are similar. Find the height of prism B. Answer: 4.5 in.

78 Doll Houses Lita made a model of her fish tank for her doll house. The model is exactly the size of the original fish tank, whose dimensions are cm. What is the volume of the model? Explore You know the scale factor and the volume of the fish tank is

79 Plan Since the volumes have a ratio of and b with 25 in., replace a with 1 Solve Write the ratio of volumes. Replace a with 1 and b with 25.

80 Simplify. So, the volume of the tank is 15,625 times the volume of the model. Answer: The volume of the model is or about 8.8 cubic centimeters.

81 Examine Check your answer by finding the dimensions of the model. Next, find the volume of the model using these dimensions.

82 Trains A scale model of a railroad boxcar is in the shape of a rectangular prism and is the size of the actual boxcar. The scale model has a volume of 72 cubic inches. What is the volume of the actual boxcar? Answer: 9,000,000 in 3

83

84 Click the mouse button or press the Space Bar to display the answers.

85 Example 1 Identify Precision Units Example 2 Identify Significant Digits Example 3 Add Measurements Example 4 Multiply Measurements

86 Identify the precision unit of the thermometer shown on the right. Answer: The precision unit is 5 F.

87 Identify the precision unit of the ruler shown on the right. Answer:

88 Determine the number of significant digits in 1040 miles. Answer: 3 significant digits

89 Determine the number of significant digits in centimeter. Answer: 1 significant digit

90 Determine the number of significant digits in kilograms. Answer: 5 significant digits

91 Determine the number of significant digits in liter. Answer: 4 significant digits

92 Determine the number of significant digits in each measure. a inches b mile c centimeters d meters Answer: 4 Answer: 1 Answer: 2 Answer: 3

93 The sides of a quadrilateral measure 0.6 meter, meter, meter, and meter. Use the correct number of significant digits to find the perimeter decimal place decimal places decimal places decimal places The least precise measurement, 0.6, has one decimal place. So, round to one decimal place, 0.8. Answer: The perimeter of the quadrilateral is about 0.8 meter.

94 The sides of a triangle measure 2.04 centimeters, 3.2 centimeters, and centimeters. Use the correct number of significant digits to find the perimeter. Answer: 7.9 cm

95 What is the area of the bedroom shown here? To find the area, multiply the length and the width significant digits x 14 2 significant digits significant digits

96 The answer cannot have more significant digits than the measurements of the length and width. So, round square feet to 2 significant digits. Answer: The area of the bedroom is about 170 square feet.

97 Suppose a bedroom was feet wide and 12.5 feet long. What would be the area of the bedroom? Answer: 171 ft 2

98

99 Explore online information about the information introduced in this chapter. Click on the Connect button to launch your browser and go to the Pre-Algebra Web site. At this site, you will find extra examples for each lesson in the Student Edition of your textbook. When you finish exploring, exit the browser program to return to this presentation. If you experience difficulty connecting to the Web site, manually launch your Web browser and go to

100

### Pre-Algebra Interactive Chalkboard Copyright by The McGraw-Hill Companies, Inc. Send all inquiries to:

Pre-Algebra Interactive Chalkboard Copyright by The McGraw-Hill Companies, Inc. Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240 Click the mouse button

### VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region.

Math 6 NOTES 7.5 Name VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region. **The formula for the volume of a rectangular prism is:** l = length w = width h = height Study Tip:

### Area of Parallelograms, Triangles, and Trapezoids (pages 314 318)

Area of Parallelograms, Triangles, and Trapezoids (pages 34 38) Any side of a parallelogram or triangle can be used as a base. The altitude of a parallelogram is a line segment perpendicular to the base

### Area of Parallelograms (pages 546 549)

A Area of Parallelograms (pages 546 549) A parallelogram is a quadrilateral with two pairs of parallel sides. The base is any one of the sides and the height is the shortest distance (the length of a perpendicular

### Pre-Algebra Interactive Chalkboard Copyright by The McGraw-Hill Companies, Inc. Send all inquiries to:

Pre-Algebra Interactive Chalkboard Copyright by The McGraw-Hill Companies, Inc. Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240 Click the mouse button

### 12-4 Volumes of Prisms and Cylinders. Find the volume of each prism. The volume V of a prism is V = Bh, where B is the area of a base and h

Find the volume of each prism. The volume V of a prism is V = Bh, where B is the area of a base and h The volume is 108 cm 3. The volume V of a prism is V = Bh, where B is the area of a base and h the

### Surface Area of Rectangular & Right Prisms Surface Area of Pyramids. Geometry

Surface Area of Rectangular & Right Prisms Surface Area of Pyramids Geometry Finding the surface area of a prism A prism is a rectangular solid with two congruent faces, called bases, that lie in parallel

### Chapter 8. Chapter 8 Opener. Section 8.1. Big Ideas Math Green Worked-Out Solutions. Try It Yourself (p. 353) Number of cubes: 7

Chapter 8 Opener Try It Yourself (p. 5). The figure is a square.. The figure is a rectangle.. The figure is a trapezoid. g. Number cubes: 7. a. Sample answer: 4. There are 5 6 0 unit cubes in each layer.

### In Problems #1 - #4, find the surface area and volume of each prism.

Geometry Unit Seven: Surface Area & Volume, Practice In Problems #1 - #4, find the surface area and volume of each prism. 1. CUBE. RECTANGULAR PRISM 9 cm 5 mm 11 mm mm 9 cm 9 cm. TRIANGULAR PRISM 4. TRIANGULAR

### Precision and Measurement

NAME DATE PERIOD Precision and Measurement The precision or exactness of a measurement depends on the unit of measure. The precision unit is the smallest unit on a measuring tool. Significant digits include

### Grade 9 Mathematics Unit 3: Shape and Space Sub Unit #1: Surface Area. Determine the area of various shapes Circumference

1 P a g e Grade 9 Mathematics Unit 3: Shape and Space Sub Unit #1: Surface Area Lesson Topic I Can 1 Area, Perimeter, and Determine the area of various shapes Circumference Determine the perimeter of various

### Name: Date: Geometry Honors Solid Geometry. Name: Teacher: Pd:

Name: Date: Geometry Honors 2013-2014 Solid Geometry Name: Teacher: Pd: Table of Contents DAY 1: SWBAT: Calculate the Volume of Prisms and Cylinders Pgs: 1-6 HW: Pgs: 7-10 DAY 2: SWBAT: Calculate the Volume

### 2nd Semester Geometry Final Exam Review

Class: Date: 2nd Semester Geometry Final Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The owner of an amusement park created a circular

### Area of a triangle: The area of a triangle can be found with the following formula: 1. 2. 3. 12in

Area Review Area of a triangle: The area of a triangle can be found with the following formula: 1 A 2 bh or A bh 2 Solve: Find the area of each triangle. 1. 2. 3. 5in4in 11in 12in 9in 21in 14in 19in 13in

### Lesson 17 ~ Volume of Prisms

Lesson 17 ~ Volume of Prisms 1. An octagonal swimming pool has a base area of 42 square meters. The pool is 3 feet deep. Find the volume of the pool. 2. A fish aquarium is a rectangular prism. It is 18

### SURFACE AREA AND VOLUME

SURFACE AREA AND VOLUME In this unit, we will learn to find the surface area and volume of the following threedimensional solids:. Prisms. Pyramids 3. Cylinders 4. Cones It is assumed that the reader has

### 8-8 Volume and Surface Area of Composite Figures. Find the volume of the composite figure. Round to the nearest tenth if necessary.

Find the volume of the composite figure. Round to the nearest tenth if necessary. The figure is made up of a triangular prism and a rectangular prism. Volume of triangular prism The figure is made up of

### SA B 1 p where is the slant height of the pyramid. V 1 3 Bh. 3D Solids Pyramids and Cones. Surface Area and Volume of a Pyramid

Accelerated AAG 3D Solids Pyramids and Cones Name & Date Surface Area and Volume of a Pyramid The surface area of a regular pyramid is given by the formula SA B 1 p where is the slant height of the pyramid.

### B = 1 14 12 = 84 in2. Since h = 20 in then the total volume is. V = 84 20 = 1680 in 3

45 Volume Surface area measures the area of the two-dimensional boundary of a threedimensional figure; it is the area of the outside surface of a solid. Volume, on the other hand, is a measure of the space

### 10.4 Surface Area of Prisms, Cylinders, Pyramids, Cones, and Spheres. 10.4 Day 1 Warm-up

10.4 Surface Area of Prisms, Cylinders, Pyramids, Cones, and Spheres 10.4 Day 1 Warm-up 1. Which identifies the figure? A rectangular pyramid B rectangular prism C cube D square pyramid 3. A polyhedron

### Solids. Objective A: Volume of a Solids

Solids Math00 Objective A: Volume of a Solids Geometric solids are figures in space. Five common geometric solids are the rectangular solid, the sphere, the cylinder, the cone and the pyramid. A rectangular

### Show that when a circle is inscribed inside a square the diameter of the circle is the same length as the side of the square.

Week & Day Week 6 Day 1 Concept/Skill Perimeter of a square when given the radius of an inscribed circle Standard 7.MG:2.1 Use formulas routinely for finding the perimeter and area of basic twodimensional

### Perfume Packaging. Ch 5 1. Chapter 5: Solids and Nets. Chapter 5: Solids and Nets 279. The Charles A. Dana Center. Geometry Assessments Through

Perfume Packaging Gina would like to package her newest fragrance, Persuasive, in an eyecatching yet cost-efficient box. The Persuasive perfume bottle is in the shape of a regular hexagonal prism 10 centimeters

### Perimeter, Area, and Volume

Perimeter, Area, and Volume Perimeter of Common Geometric Figures The perimeter of a geometric figure is defined as the distance around the outside of the figure. Perimeter is calculated by adding all

### Height. Right Prism. Dates, assignments, and quizzes subject to change without advance notice.

Name: Period GL UNIT 11: SOLIDS I can define, identify and illustrate the following terms: Face Isometric View Net Edge Polyhedron Volume Vertex Cylinder Hemisphere Cone Cross section Height Pyramid Prism

### 10-4 Surface Area of Prisms and Cylinders

: Finding Lateral Areas and Surface Areas of Prisms 2. Find the lateral area and surface area of the right rectangular prism. : Finding Lateral Areas and Surface Areas of Right Cylinders 3. Find the lateral

### Teacher Page Key. Geometry / Day # 13 Composite Figures 45 Min.

Teacher Page Key Geometry / Day # 13 Composite Figures 45 Min. 9-1.G.1. Find the area and perimeter of a geometric figure composed of a combination of two or more rectangles, triangles, and/or semicircles

### CONNECT: Volume, Surface Area

CONNECT: Volume, Surface Area 1. VOLUMES OF SOLIDS A solid is a three-dimensional (3D) object, that is, it has length, width and height. One of these dimensions is sometimes called thickness or depth.

### Area is a measure of how much space is occupied by a figure. 1cm 1cm

Area Area is a measure of how much space is occupied by a figure. Area is measured in square units. For example, one square centimeter (cm ) is 1cm wide and 1cm tall. 1cm 1cm A figure s area is the number

### Area of a triangle: The area of a triangle can be found with the following formula: You can see why this works with the following diagrams:

Area Review Area of a triangle: The area of a triangle can be found with the following formula: 1 A 2 bh or A bh 2 You can see why this works with the following diagrams: h h b b Solve: Find the area of

### 1. Kyle stacks 30 sheets of paper as shown to the right. Each sheet weighs about 5 g. How can you find the weight of the whole stack?

Prisms and Cylinders Answer Key Vocabulary: cylinder, height (of a cylinder or prism), prism, volume Prior Knowledge Questions (Do these BEFORE using the Gizmo.) [Note: The purpose of these questions is

### ACTIVITY: Finding a Formula Experimentally. Work with a partner. Use a paper cup that is shaped like a cone.

8. Volumes of Cones How can you find the volume of a cone? You already know how the volume of a pyramid relates to the volume of a prism. In this activity, you will discover how the volume of a cone relates

### Geometry Honors: Extending 2 Dimensions into 3 Dimensions. Unit Overview. Student Focus. Semester 2, Unit 5: Activity 30. Resources: Online Resources:

Geometry Honors: Extending 2 Dimensions into 3 Dimensions Semester 2, Unit 5: Activity 30 Resources: SpringBoard- Geometry Online Resources: Geometry Springboard Text Unit Overview In this unit students

### Geometry and Measurement

The student will be able to: Geometry and Measurement 1. Demonstrate an understanding of the principles of geometry and measurement and operations using measurements Use the US system of measurement for

### Honors Geometry Final Exam Study Guide

2011-2012 Honors Geometry Final Exam Study Guide Multiple Choice Identify the choice that best completes the statement or answers the question. 1. In each pair of triangles, parts are congruent as marked.

### Integrated Algebra: Geometry

Integrated Algebra: Geometry Topics of Study: o Perimeter and Circumference o Area Shaded Area Composite Area o Volume o Surface Area o Relative Error Links to Useful Websites & Videos: o Perimeter and

### CHAPTER 8, GEOMETRY. 4. A circular cylinder has a circumference of 33 in. Use 22 as the approximate value of π and find the radius of this cylinder.

TEST A CHAPTER 8, GEOMETRY 1. A rectangular plot of ground is to be enclosed with 180 yd of fencing. If the plot is twice as long as it is wide, what are its dimensions? 2. A 4 cm by 6 cm rectangle has

### SOLID SHAPES M.K. HOME TUITION. Mathematics Revision Guides Level: GCSE Higher Tier

Mathematics Revision Guides Solid Shapes Page 1 of 19 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Higher Tier SOLID SHAPES Version: 2.1 Date: 10-11-2015 Mathematics Revision Guides Solid

### Finding Volume of Rectangular Prisms

MA.FL.7.G.2.1 Justify and apply formulas for surface area and volume of pyramids, prisms, cylinders, and cones. MA.7.G.2.2 Use formulas to find surface areas and volume of three-dimensional composite shapes.

### Volume of Spheres. A geometric plane passing through the center of a sphere divides it into. into the Northern Hemisphere and the Southern Hemisphere.

Page 1 of 7 9.6 Surface Area and Volume of Spheres Goal Find surface areas and volumes of spheres. Key Words sphere hemisphere A globe is an example of a sphere. A sphere is the set of all points in space

### Let s find the volume of this cone. Again we can leave our answer in terms of pi or use 3.14 to approximate the answer.

8.5 Volume of Rounded Objects A basic definition of volume is how much space an object takes up. Since this is a three-dimensional measurement, the unit is usually cubed. For example, we might talk about

### Demystifying Surface Area and Volume Teachers Edition

Demystifying Surface and Volume Teachers Edition These constructions and worksheets can be done in pairs, small groups or individually. Also, may use as guided notes and done together with teacher. CYLINDER

### 12-1 Representations of Three-Dimensional Figures

Connect the dots on the isometric dot paper to represent the edges of the solid. Shade the tops of 12-1 Representations of Three-Dimensional Figures Use isometric dot paper to sketch each prism. 1. triangular

### 12-2 Surface Areas of Prisms and Cylinders. 1. Find the lateral area of the prism. SOLUTION: ANSWER: in 2

1. Find the lateral area of the prism. 3. The base of the prism is a right triangle with the legs 8 ft and 6 ft long. Use the Pythagorean Theorem to find the length of the hypotenuse of the base. 112.5

### Surface Area and Volume

1 Area Surface Area and Volume 8 th Grade 10 days by Jackie Gerwitz-Dunn and Linda Kelly 2 What do you want the students to understand at the end of this lesson? The students should be able to distinguish

### Surface Area of Prisms

Surface Area of Prisms Find the Surface Area for each prism. Show all of your work. Surface Area: The sum of the areas of all the surface (faces) if the threedimensional figure. Rectangular Prism: A prism

### Pizza! Pizza! Assessment

Pizza! Pizza! Assessment 1. A local pizza restaurant sends pizzas to the high school twelve to a carton. If the pizzas are one inch thick, what is the volume of the cylindrical shipping carton for the

### Geometry Review. Here are some formulas and concepts that you will need to review before working on the practice exam.

Geometry Review Here are some formulas and concepts that you will need to review before working on the practice eam. Triangles o Perimeter or the distance around the triangle is found by adding all of

### *1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles.

Students: 1. Students understand and compute volumes and areas of simple objects. *1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles. Review

### Surface Area of Prisms

Surface Area of Prisms Jen Kershaw Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of this book, as well as other interactive content,

Performance Based Learning and Assessment Task Confetti Task I. ASSESSMENT TASK OVERVIEW & PURPOSE: In this task, Geometry students will investigate how surface area and volume is used to estimate the

### Geometry Unit 6 Areas and Perimeters

Geometry Unit 6 Areas and Perimeters Name Lesson 8.1: Areas of Rectangle (and Square) and Parallelograms How do we measure areas? Area is measured in square units. The type of the square unit you choose

### Lateral and Surface Area of Right Prisms

CHAPTER A Lateral and Surface Area of Right Prisms c GOAL Calculate lateral area and surface area of right prisms. You will need a ruler a calculator Learn about the Math A prism is a polyhedron (solid

### Surface Area and Volume Nets to Prisms

Surface Area and Volume Nets to Prisms Michael Fauteux Rosamaria Zapata CK12 Editor Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version

### Areas of Rectangles and Parallelograms

CONDENSED LESSON 8.1 Areas of Rectangles and Parallelograms In this lesson you will Review the formula for the area of a rectangle Use the area formula for rectangles to find areas of other shapes Discover

### 1. A plane passes through the apex (top point) of a cone and then through its base. What geometric figure will be formed from this intersection?

Student Name: Teacher: Date: District: Description: Miami-Dade County Public Schools Geometry Topic 7: 3-Dimensional Shapes 1. A plane passes through the apex (top point) of a cone and then through its

### Geometry Notes PERIMETER AND AREA

Perimeter and Area Page 1 of 57 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter

### A. 32 cu ft B. 49 cu ft C. 57 cu ft D. 1,145 cu ft. F. 96 sq in. G. 136 sq in. H. 192 sq in. J. 272 sq in. 5 in

7.5 The student will a) describe volume and surface area of cylinders; b) solve practical problems involving the volume and surface area of rectangular prisms and cylinders; and c) describe how changing

### MENSURATION. Definition

MENSURATION Definition 1. Mensuration : It is a branch of mathematics which deals with the lengths of lines, areas of surfaces and volumes of solids. 2. Plane Mensuration : It deals with the sides, perimeters

### 12 Surface Area and Volume

12 Surface Area and Volume 12.1 Three-Dimensional Figures 12.2 Surface Areas of Prisms and Cylinders 12.3 Surface Areas of Pyramids and Cones 12.4 Volumes of Prisms and Cylinders 12.5 Volumes of Pyramids

### 17.2 Surface Area of Prisms and Cylinders

Name Class Date 17. Surface Area of Prisms and Cylinders Essential Question: How can you find the surface area of a prism or cylinder? Explore G.11.C Apply the formulas for the total and lateral surface

### of surface, 569-571, 576-577, 578-581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433

Absolute Value and arithmetic, 730-733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property

### Calculating the surface area of a three-dimensional object is similar to finding the area of a two dimensional object.

Calculating the surface area of a three-dimensional object is similar to finding the area of a two dimensional object. Surface area is the sum of areas of all the faces or sides of a three-dimensional

### FSA Geometry End-of-Course Review Packet. Modeling and Geometry

FSA Geometry End-of-Course Review Packet Modeling and Geometry MAFS.912.G-MG.1.1 EOC Practice Level 2 Level 3 Level 4 Level 5 uses measures and properties to model and describe a realworld object that

### Unit 3 Practice Test. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

Name: lass: ate: I: Unit 3 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. The radius, diameter, or circumference of a circle is given. Find

### What You ll Learn. Why It s Important

These students are setting up a tent. How do the students know how to set up the tent? How is the shape of the tent created? How could students find the amount of material needed to make the tent? Why

### Week #15 - Word Problems & Differential Equations Section 8.1

Week #15 - Word Problems & Differential Equations Section 8.1 From Calculus, Single Variable by Hughes-Hallett, Gleason, McCallum et. al. Copyright 25 by John Wiley & Sons, Inc. This material is used by

### Practice: Space Figures and Cross Sections Geometry 11-1

Practice: Space Figures and Cross Sections Geometry 11-1 Name: Date: Period: Polyhedron * 3D figure whose surfaces are * each polygon is a. * an is a segment where two faces intersect. * a is a point where

### Scope and Sequence KA KB 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B

Scope and Sequence Earlybird Kindergarten, Standards Edition Primary Mathematics, Standards Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced

### Right Prisms Let s find the surface area of the right prism given in Figure 44.1. Figure 44.1

44 Surface Area The surface area of a space figure is the total area of all the faces of the figure. In this section, we discuss the surface areas of some of the space figures introduced in Section 41.

### b = base h = height Area is the number of square units that make up the inside of the shape is a square with a side length of 1 of any unit

Area is the number of square units that make up the inside of the shape of 1 of any unit is a square with a side length Jan 29-7:58 AM b = base h = height Jan 29-8:31 AM 1 Example 6 in Jan 29-8:33 AM A

### S.A. = L.A. + 2B = ph + 2B

Page 1 of 5 View Tutorial 5c Objective: Find the lateral area, total surface area, and volume of rectangular prisms. A prism is a polyhedron with two congruent & parallel bases. The other faces are the

### 3. If AC = 12, CD = 9 and BE = 3, find the area of trapezoid BCDE. (Mathcounts Handbooks)

EXERCISES: Triangles 1 1. The perimeter of an equilateral triangle is units. How many units are in the length 27 of one side? (Mathcounts Competitions) 2. In the figure shown, AC = 4, CE = 5, DE = 3, and

### Geometry Notes VOLUME AND SURFACE AREA

Volume and Surface Area Page 1 of 19 VOLUME AND SURFACE AREA Objectives: After completing this section, you should be able to do the following: Calculate the volume of given geometric figures. Calculate

### Scaling Three-Dimensional Figures

exploration Scaling Three-Dimensional Figures A rectangular box can be scaled up by increasing one of its three dimensions. To increase one dimension of the box, multiply the dimension by a scale factor.

### WEIGHTS AND MEASURES. Linear Measure. 1 Foot12 inches. 1 Yard 3 feet - 36 inches. 1 Rod 5 1/2 yards - 16 1/2 feet

WEIGHTS AND MEASURES Linear Measure 1 Foot12 inches 1 Yard 3 feet - 36 inches 1 Rod 5 1/2 yards - 16 1/2 feet 1 Furlong 40 rods - 220 yards - 660 feet 1 Mile 8 furlongs - 320 rods - 1,760 yards 5,280 feet

### Surface Area. Assessment Management

Surface Area Objective To introduce finding the surface area of prisms, cylinders, and pyramids. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters

### CHAPTER 29 VOLUMES AND SURFACE AREAS OF COMMON SOLIDS

CHAPTER 9 VOLUMES AND SURFACE AREAS OF COMMON EXERCISE 14 Page 9 SOLIDS 1. Change a volume of 1 00 000 cm to cubic metres. 1m = 10 cm or 1cm = 10 6m 6 Hence, 1 00 000 cm = 1 00 000 10 6m = 1. m. Change

### The Area is the width times the height: Area = w h

Geometry Handout Rectangle and Square Area of a Rectangle and Square (square has all sides equal) The Area is the width times the height: Area = w h Example: A rectangle is 6 m wide and 3 m high; what

### Algebra Geometry Glossary. 90 angle

lgebra Geometry Glossary 1) acute angle an angle less than 90 acute angle 90 angle 2) acute triangle a triangle where all angles are less than 90 3) adjacent angles angles that share a common leg Example:

### Activity Set 4. Trainer Guide

Geometry and Measurement of Solid Figures Activity Set 4 Trainer Guide Mid_SGe_04_TG Copyright by the McGraw-Hill Companies McGraw-Hill Professional Development GEOMETRY AND MEASUREMENT OF SOLID FIGURES

### Unit 1 Review. Multiple Choice Identify the choice that best completes the statement or answers the question.

Unit 1 Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Convert 8 yd. to inches. a. 24 in. b. 288 in. c. 44 in. d. 96 in. 2. Convert 114 in. to yards,

### Review for Final - Geometry B

Review for Final - Geometry B Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A model is made of a car. The car is 4 meters long and the model is 7 centimeters

### CONNECT: Volume, Surface Area

CONNECT: Volume, Surface Area 2. SURFACE AREAS OF SOLIDS If you need to know more about plane shapes, areas, perimeters, solids or volumes of solids, please refer to CONNECT: Areas, Perimeters 1. AREAS

### Chapter 4: Area, Perimeter, and Volume. Geometry Assessments

Chapter 4: Area, Perimeter, and Volume Geometry Assessments Area, Perimeter, and Volume Introduction The performance tasks in this chapter focus on applying the properties of triangles and polygons to

### 11-4 Areas of Regular Polygons and Composite Figures

1. In the figure, square ABDC is inscribed in F. Identify the center, a radius, an apothem, and a central angle of the polygon. Then find the measure of a central angle. Center: point F, radius:, apothem:,

### 1. Find the surface area and volume: 9 in Unit Three Problem

1. Find the surface area and volume: 9 in. 3.5 2. Find the surface area and volume: 3 in. 3 in. 8 in. 3 in. 3 in. 8 in. 9 in. 3. A sketch of the Surenkov home is shown in the following figure, with the

### Sandia High School Geometry Second Semester FINAL EXAM. Mark the letter to the single, correct (or most accurate) answer to each problem.

Sandia High School Geometry Second Semester FINL EXM Name: Mark the letter to the single, correct (or most accurate) answer to each problem.. What is the value of in the triangle on the right?.. 6. D.

### 1 foot (ft) = 12 inches (in) 1 yard (yd) = 3 feet (ft) 1 mile (mi) = 5280 feet (ft) Replace 1 with 1 ft/12 in. 1ft

2 MODULE 6. GEOMETRY AND UNIT CONVERSION 6a Applications The most common units of length in the American system are inch, foot, yard, and mile. Converting from one unit of length to another is a requisite

### Fundamentals of Geometry

10A Page 1 10 A Fundamentals of Geometry 1. The perimeter of an object in a plane is the length of its boundary. A circle s perimeter is called its circumference. 2. The area of an object is the amount

### Area, Perimeter, Surface Area and Change Overview

Area, Perimeter, Surface Area and Change Overview Enduring Understanding: (5)ME01: Demonstrate understanding of the concept of area (5)ME02: Demonstrate understanding of the differences between length

### PERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures.

PERIMETER AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures. Perimeter Perimeter The perimeter of a polygon, denoted by P, is the

### Unit 8 Geometry. Introduction. Materials

Unit 8 Geometry Introduction In this unit, students will learn about volume and surface area. As they find the volumes of prisms and the surface areas of prisms and pyramids, students will add, subtract,

### Area & Volume. 1. Surface Area to Volume Ratio

1 1. Surface Area to Volume Ratio Area & Volume For most cells, passage of all materials gases, food molecules, water, waste products, etc. in and out of the cell must occur through the plasma membrane.

### GAP CLOSING. Volume and Surface Area. Intermediate / Senior Student Book

GAP CLOSING Volume and Surface Area Intermediate / Senior Student Book Volume and Surface Area Diagnostic...3 Volumes of Prisms...6 Volumes of Cylinders...13 Surface Areas of Prisms and Cylinders...18

### Volume of Rectangular Prisms Objective To provide experiences with using a formula for the volume of rectangular prisms.

Volume of Rectangular Prisms Objective To provide experiences with using a formula for the volume of rectangular prisms. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts

### Surface Areas of Prisms and Cylinders

12.2 TEXAS ESSENTIAL KNOWLEDGE AND SKILLS G.10.B G.11.C Surface Areas of Prisms and Cylinders Essential Question How can you find te surface area of a prism or a cylinder? Recall tat te surface area of

### Platonic Solids. Some solids have curved surfaces or a mix of curved and flat surfaces (so they aren't polyhedra). Examples:

Solid Geometry Solid Geometry is the geometry of three-dimensional space, the kind of space we live in. Three Dimensions It is called three-dimensional or 3D because there are three dimensions: width,