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Lesson 7-1 Circumference and Area of Circles Lesson 7-2 Problem-Solving Investigation: Solve a Simpler Problem Lesson 7-3 Area of Composite Figures Lesson 7-4 Three-Dimensional Figures Lesson 7-5 Volume of Prisms and Cylinders Lesson 7-6 Volume of Pyramids, Cones, and Spheres Lesson 7-7 Surface Area of Prisms and Cylinders Lesson 7-8 Surface Area of Pyramids Lesson 7-9 Similar Solids Chapter Menu

Five-Minute Check (over Chapter 6) Main Idea and Vocabulary Targeted TEKS Key Concept: Circumference of a Circle Example 1: Find the Circumferences of Circles Example 2: Find the Circumferences of Circles Key Concept: Area of a Circle Example 3: Find the Areas of Circles Example 4: Find the Areas of Circles Example 5: Real-World Example Lesson 1 Menu

Find the circumference and area of circles. Center Radius Diameter Circumference Pi Lesson 1 MI/Vocab

C I R C U M F E R E N C E π ≈ 3.14 ≈ 22/7 Vocabulary Circle – All points that are the same distance from another point Pi – Ratio of Circumference Diameter π ≈ 3.14 ≈ 22/7 Radius D i a m e t e r Center C I R C U M F E R E N C E B

d=diameter and r=radius A= π r2 r=radius NOTES USE THIS PROCESS to solve problems in Chapter 7 WRITE down the correct formula PLUG in what you know SOLVE for what you don’t CIRCUMFERENCE of a circle C= π d or C= 2 π r d=diameter and r=radius AREA of a circle A= π r2 r=radius Lesson 1 TEKS

Lesson 1 Key Concept 1

Find the Circumferences of Circles Find the circumference of the circle. Round to the nearest tenth. C = d Circumference of a circle C =   5 Replace d with 5. C = 5 This is the exact circumference. Use a calculator to find 5. 5 15.70796327  × ENTER = Answer: The circumference is about 15.7 feet. Lesson 1 Ex1

Find the circumference of the circle. Round to the nearest tenth. A. 38.5 in. B. 31.4 in. C. 22.0 in. D. 19.7 in. A B C D Lesson 1 CYP1

Find the Circumferences of Circles Find the circumference of the circle. Round to the nearest tenth. C = 2r Circumference of a circle C = 2    3.8 Replace r with 3.8. C ≈ 23.9 Use a calculator. Answer: The circumference is about 23.9 meters. Lesson 1 Ex2

Find the circumference of the circle. Round to the nearest tenth. A. 9.4 m B. 11.3 m C. 18.5 m D. 22.6 m A B C D Lesson 1 CYP2

Lesson 1 Key Concept 2

Find the Areas of Circles Find the area of the circle. Round to the nearest tenth. A = r2 Area of a circle A =   32 Replace r with 3. A =   9 Evaluate 32. A ≈ 28.3 Use a calculator. Answer: The area is about 28.3 square yards. Lesson 1 Ex3

Find the area of the circle. Round to the nearest tenth. A. 12.6 ft2 B. 14.1 ft2 C. 15.3 ft2 D. 17.4 ft2 A B C D Lesson 1 CYP3

Find the Areas of Circles Find the area of the circle. Round to the nearest tenth. A = r2 Area of a circle A =   52 Replace r with half of 10 or 5. A =   25 Evaluate 52. A ≈ 78.5 Use a calculator. Answer: The area is about 78.5 square inches. Lesson 1 Ex4

Find the area of the circle. Round to the nearest tenth. A. 42.7 cm2 B. 50.3 cm2 C. 52.1 cm2 D. 54.6 cm2 A B C D Lesson 1 CYP4

POOLS The Patels have a circular pool with a radius of 12 feet POOLS The Patels have a circular pool with a radius of 12 feet. They plan on installing a 4-foot-wide walkway around the pool. What will be the area of the walkway? To determine the area of the walkway, you must subtract the area of the pool from the area of the outer circle that includes the pool and the walkway. Lesson 1 Ex5

A = (16)2 Replace r with 12 + 4 or 16. A =   256 Evaluate 162. Area of Outer Circle A = r2 Area of a circle A = (16)2 Replace r with 12 + 4 or 16. A =   256 Evaluate 162. Lesson 1 Ex5

Area of Pool A = r2 Area of a circle A =   122 Replace r with 12. A =   144 Evaluate 122. Lesson 1 Ex5

Area of Walkway = Area of Outer Circle – Area of Pool ≈ 256 – 144 ≈ 351.9 Answer: The area of the walkway is about 351.9 square feet. Lesson 1 Ex5

POOLS The Shoemakers have a circular pond with a radius of 4 feet POOLS The Shoemakers have a circular pond with a radius of 4 feet. They plan on installing a 2-foot-wide walkway around the pond. What will be the area of the walkway? A. 62.8 ft2 B. 84.3 ft2 C. 99.2 ft2 D. 113.1 ft2 A B C D Lesson 1 CYP5

End of Lesson 1

Five-Minute Check (over Lesson 7-1) Main Idea Targeted TEKS Example 1: Solve a Simpler Problem Lesson 2 Menu

Solve a simpler problem. Lesson 2 MI/Vocab

8.14 The student applies Grade 8 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. (C) Select or develop an appropriate problem-solving strategy from a variety of different types, including…working a simpler problem…to solve a problem. Lesson 2 TEKS

Solve a Simpler Problem GARDENS A series of gardens framed by tiles is arranged such that each successive garden is one tile longer than the previous garden. The width of the gardens is four tiles. The first three gardens are shown below. How many tiles surround Garden 10? Explore You know how many tiles surround the first three gardens. Use this information to predict how many tiles will surround Garden 10. Lesson 2 Ex1

Solve a Simpler Problem Plan It would take a long time to draw each of the first 10 gardens. Instead, find the number of tiles surrounding the smaller gardens and look for a pattern. Solve For each successive garden, an additional 2 tiles are needed to surround it. The 10th garden will be surrounded by 16 + 2 + 2 + 2 + 2 + 2 + 2 or 28 tiles. Check Check your answer by drawing Garden 10. Lesson 2 Ex1

GAMES The figures below show the number of tiles on a game board after the first 4 rounds of the game. Each round, the same number of tiles are added to the board. How many tiles will be on the board after the 12th round? A B C D A. 37 tiles B. 41 tiles C. 45 tiles D. 53 tiles Lesson 2 CYP1

End of Lesson 2

Five-Minute Check (over Lesson 7-2) Main Idea and Vocabulary Targeted TEKS Example 1: Find the Area of a Composite Figure Example 2: Real-World Example Lesson 3 Menu

Find the area of composite figures. A figure made up of 2 or more shapes Lesson 3 MI/Vocab

NOTES To find the area of composite figures Draw lines to break the figure up into parts Find the area of the parts Add (or subtract) all the areas THE BASE AND THE HEIGHT MUST FORM A RIGHT ANGLE! Parallelogram A = bh Triangle A = ½ bh b = base h = ACTUAL height b = base h = ACTUAL height Lesson 3 TEKS

NOTES – Continued Trapezoid Circle A = π r2 A = ½ (b1 + b2) * h b2 = base2 h = ACTUAL height b1 = base1 r = radius Lesson 3 TEKS

Lesson 3 Key Concept 1

Find the Area of a Composite Figure Find the area of the complex figure. Round to the nearest tenth. The figure can be separated into two semicircles and a rectangle. Lesson 3 Ex1

Find the Area of a Composite Figure Area of semicircles Area of rectangle Answer: The area of the figure is about 28.3 + 72 or 100.3 square centimeters. Lesson 3 Ex1

Find the area of the complex figure. Round to the nearest tenth. A. 15.6 ft2 B. 16.2 ft2 C. 16.8 ft2 D. 17.1 ft2 A B C D Lesson 3 CYP1

GARDENING The dimensions of a flower garden are shown GARDENING The dimensions of a flower garden are shown. What is the area of the garden? The garden can be separated into a rectangle and two congruent triangles. Lesson 3 Ex2

Answer: The area of the garden is 35 + 5 + 5 or 45 square feet. Area of rectangle Area of one triangle Answer: The area of the garden is 35 + 5 + 5 or 45 square feet. Lesson 3 Ex2

GARDENING The dimensions of a flower garden are shown GARDENING The dimensions of a flower garden are shown. What is the area of the garden? A. 48 ft2 B. 56 ft2 C. 64 ft2 D. 70 ft2 A B C D Lesson 3 CYP2

End of Lesson 3

Five-Minute Check (over Lesson 7-3) Main Idea and Vocabulary Targeted TEKS Key Concept: Common Polyhedrons Example 1: Identify Prisms and Pyramids Example 2: Identify Prisms and Pyramids Example 3: Analyze Drawings Example 4: Draw a Three-Dimensional Figure Lesson 4 Menu

Identify and draw three-dimensional figures. Plane Flat surface that goes forever in all directions ( a whiteboard) Polyhedron Solid with sides that are polygons Prism Polyhedron with 2 parallel IDENTICAL sides Base Gives the polyhedron it’s shape Pyramid Base is a polygon, sides are triangles Lesson 4 MI/Vocab

Vocabulary – Cont. Base = WHAT GIVES A PRISM IT’S NAME! Face = flat surface Vertex = point edge = line Lesson 4 TEKS

NOTES Prisms Drawing 3-D Figures They have TWO bases! Are named by the shape of their BASE!! Determine base by answering one of the following questions: “If I stand it on its end and fill it with water, WHAT WILL THE WATER HIT FIRST?” “If I sliced it like bread, what shape would the bread be?” Drawing 3-D Figures Turn figure to look at it from front, top, side, and back. Draw what you see. Lesson 4 TEKS

Lesson 4 Key Concept 1

Identify Prisms and Pyramids Identify the solid. Name the number and shapes of the faces. Then name the number of edges and vertices. Answer: The figure has two parallel congruent bases that are octagons, so it is an octagonal prism. The other eight faces are rectangles. It has a total of 10 faces, 24 edges, and 16 vertices. Lesson 4 Ex1

Identify the solid. Name the number and shapes of the faces Identify the solid. Name the number and shapes of the faces. Then name the number of edges and vertices. Answer: triangular prism; 2 triangular faces, 3 rectangular faces, 9 edges, and 6 vertices Lesson 4 CYP1

Identify Prisms and Pyramids Identify the solid. Name the number and shapes of the faces. Then name the number of edges and vertices. Answer: The figure has one base that is a rectangle, so it is a rectangular pyramid. The other four faces are triangles. It has a total of 5 faces, 8 edges, and 5 vertices. Lesson 4 Ex2

Identify the solid. Name the number and shapes of the faces Identify the solid. Name the number and shapes of the faces. Then name the number of edges and vertices. Answer: pentagonal pyramid; 1 pentagonal base, 5 triangular faces, 10 edges, and 6 vertices Lesson 4 Ex2

Analyze Drawings ARCHITECTURE The plans for a hotel fireplace are shown below. Draw and label the top, front, and side views. Answer: Lesson 4 Ex3

ARCHITECTURE The plans for a building are shown below ARCHITECTURE The plans for a building are shown below. Draw and label the top, front, and side views. Answer: Lesson 4 CYP3

Draw a Three-Dimensional Figure The top-count view of a three-dimensional figure is shown. Draw the figure on isometric dot paper. The greatest number on the top-count view is 3. Therefore, the height of the solid is 3 units, and it has three layers. Draw each layer one at a time, adding the appropriate number of cubes. Answer: Lesson 4 Ex4

The top-count view of a three-dimensional figure is shown below The top-count view of a three-dimensional figure is shown below. Draw the figure on isometric dot paper. The greatest number on the top-count view is 4. Therefore, the height of the solid is 4 units, and it has four layers. Draw each layer one at a time, adding the appropriate number of cubes. Answer: Lesson 4 CYP4

End of Lesson 4

Five-Minute Check (over Lesson 7-4) Main Idea and Vocabulary Targeted TEKS Key Concept: Volume of a Prism Example 1: Find the Volumes of Prisms Example 2: Find the Volumes of Prisms Key Concept: Volume of a Cylinder Example 3: Find the Volume of a Cylinder Example 4: Find the Volume of a Composite Solid Lesson 5 Menu

Find the volumes of prisms and cylinders. Space occupied by an object or HOW MUCH CAN I PUT IN IT? Cylinder Solid whose bases are parallel circles. composite solid Objects made up of more than one kind of solid Lesson 5 MI/Vocab

Volume of Composite Solids NOTES Volume of Prisms V = Bh B = AREA OF THE BASE!!!! MAY BE DIFFERENT FOR EACH PRISM!! h = Actual height Volume of Cylinders B = Area of a circle = πr2 V = πr2h Volume of Composite Solids Divide solid into each piece Calculate volume for each piece Add (or subtract) all the pieces to get the total volume Lesson 5 TEKS

Lesson 5 Key Concept 1

Find the Volumes of Prisms Find the volume of the prism. Volume of a prism Simplify. Answer: The volume is 385 cubic inches. Lesson 5 Ex1

Find the volume of the prism. A. 90 in3 B. 120 in3 C. 126 in3 D. 148 in3 A B C D Lesson 5 CYP1

Find the Volumes of Prisms Find the volume of the prism. Volume of a prism The base is a triangle, so B = The height of the prism is 4. Simplify. Answer: The volume is 270 cubic feet. Lesson 5 Ex2

Find the volume of the prism. A. 22 ft3 B. 30 ft3 C. 37 ft3 D. 45 ft3 A B C D Lesson 5 CYP2

Lesson 5 Key Concept 2

Find the Volume of a Cylinder Find the volume of the cylinder. Round to the nearest tenth. Volume of a cylinder Replace r with 3 and h with 12. Simplify. Answer: The volume is about 339.3 cubic centimeters. Lesson 5 Ex3

Find the volume of the cylinder. Round to the nearest tenth. A. 140.1 in3 B. 152.5 in3 C. 169.6 in3 D. 183.4 in3 A B C D Lesson 5 CYP3

Find the Volume of a Composite Solid TOYS A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth. The block is a rectangular prism with a cylindrical hole. To find the volume of the block, subtract the volume of the cylinder from the volume of the prism. Lesson 5 Ex4

Find the Volume of a Composite Solid Rectangular Prism Cylinder Answer: The volume of the box is about 72 – 9.42 or 62.58 cubic centimeters. Lesson 5 Ex4

HOBBIES A small wooden cube has been glued to a larger wooden block for a whittling project. What is the volume of the wood to be whittled? A. 98 in3 B. 104 in3 C. 112 in3 D. 115 in3 A B C D Lesson 5 CYP4

End of Lesson 5

Five-Minute Check (over Lesson 7-5) Main Idea and Vocabulary Targeted TEKS Key Concept: Volume of a Pyramid Example 1: Find the Volume of a Pyramid Example 2: Real-World Example Key Concept: Volume of a Cone Example 3: Find the Volume of a Cone Key Concept: Volume of a Sphere Example 4: Find the Volume of a Sphere Lesson 6 Menu

Find the volumes of pyramids, cones, and spheres. 3-D figure with ONE circle for a base Sphere Set of all points in 3D space the same distance from a center point (like a circle, except in 3-D) Lesson 6 MI/Vocab

Volume of a Pyramid and a Cone B = AREA of base h = ACTUAL height NOTES Volume of a Pyramid and a Cone V= 1/3 Bh = Bh/3 B = AREA of base!!! For cone B = πr2 For Pyramid B could be anything! h = ACTUAL height Volume of Sphere V=4/3 πr3 = 4 (πr3) / 3 r = radius of sphere r = radius Lesson 6 TEKS

Lesson 6 Key Concept 1

Find the Volume of a Pyramid Find the volume of the pyramid. Volume of a pyramid B = 7 ● 3, h = 20 Simplify. Answer: The volume is 140 cubic centimeters. Lesson 6 Ex1

Find the volume of the pyramid. B. 72 m3 C. 80 m3 D. 120 m3 A B C D Lesson 6 CYP1

Replace V with12 and h with 4. SOUVENIRS A novelty souvenir company wants to make snow “globes” shaped like pyramids. It decides that the most cost-effective maximum volume of water for the pyramids is 12 cubic inches. If a pyramid measures 4 inches in height, find the area of its base. Volume of a pyramid Replace V with12 and h with 4. Lesson 6 Ex2

Answer: The area of the base of the snow globe is 9 square inches. Simplify. Answer: The area of the base of the snow globe is 9 square inches. Lesson 6 Ex2

TOYS A company is designing pyramid shaped building blocks with a square base. They want the volume of the blocks to be 18 square inches. If the length of the side of the base is 3 inches, what should be the height of the blocks? A. 6 in. B. 6.5 in. C. 7 in. D. 7.5 in. A B C D Lesson 6 CYP2

Lesson 6 Key Concept 2

Find the Volume of a Cone Find the volume of the cone. Round to the nearest tenth. Volume of a cone Replace r with1.5 and h with 8. Simplify. Answer: The volume is about 18.8 cubic meters. Lesson 6 Ex3

Find the volume of the cone. Round to the nearest tenth. A. 28.5 in3 B. 29.2 in3 C. 34.1 in3 D. 37.7 in3 A B C D Lesson 6 CYP3

Lesson 6 Key Concept 3

Find the Volume of a Sphere GLOBES A school principal purchased a new globe for each classroom in the school. The radius of each globe was 6 inches. What is the volume of each globe? Round to the nearest tenth. Volume of a sphere Replace r with 6. V ≈ 904.8 Simplify. Answer: The volume of each globe is about 904.8 cubic inches. Lesson 6 Ex4

SPORTS The diameter of a tennis ball is 6. 5 centimeters SPORTS The diameter of a tennis ball is 6.5 centimeters. What is the volume of a tennis ball? Round to the nearest tenth. A. 143.8 cm3 B. 166.2 cm3 C. 174.5 cm3 D. 211.2 cm3 A B C D Lesson 6 CYP4

End of Lesson 6

Five-Minute Check (over Lesson 7-6) Main Idea and Vocabulary Targeted TEKS Key Concepts: Lateral Surface Area of a Prism Example 1: Surface Areas of a Prism Example 2: Surface Areas of a Prism Key Concepts: Lateral Surface Area of a Cylinder Example 3: Surface Areas of Cylinders Example 4: Surface Areas of Cylinders Lesson 7 Menu

Find the lateral and total surface areas of prisms and cylinders. Area that covers the ENTIRE OUTSIDE of a solid object Lateral face Any flat surface that is NOT a base! lateral surface area Add the areas of ALL lateral surfaces total surface area Add the lateral surface area PLUS the area of the bases Net A 2D drawing of a 3D object. Lesson 7 MI/Vocab

Interactive Lab: Surface Area of Prisms NOTES There are 3 ways to calculate surface area problems. Using the formula Prisms/Cylinders - S = Ph + 2B P = PERIMETER of the base h = HEIGHT of the PRISM B = AREA of base Using Nets Draw the Net Calculate the areas of the pieces Add them together Calculate the areas of each side and add them up. Lateral Surface Area S = Ph Interactive Lab: Surface Area of Prisms Lesson 7 TEKS

Lesson 7 Key Concept 1

Surface Areas of a Prism Find the lateral and total surface area of the rectangular prism. Perimeter of Base Area of Base P = 2ℓ + 2w B = ℓw P = 2(15) + 2(9) or 48 B = 15(9) or 135 Lesson 7 Ex1

Surface Areas of a Prism Use this information to find the lateral and total surface area. Lateral Surface Area Total Surface Area L = Ph S = L + 2B L = 48(7) or 336 S = 336 + 2(135) or 606 Answer: The lateral surface area is 336 square millimeters, and the total surface area is 606 square millimeters. Lesson 7 Ex1

Find the total surface area of the rectangular prism. A. 112 cm2 B. 126 cm2 C. 130 cm2 D. 142 cm2 A B C D Lesson 7 CYP1

Surface Areas of a Prism CAMPING A family wants to reinforce the fabric of its tent with a waterproofing treatment. Find the total surface area, including the floor, of the tent below. A triangular prism consists of two congruent triangular faces and three rectangular faces. Lesson 7 Ex2

Surface Areas of a Prism Draw and label a net of this prism. Find the area of each face. bottom 5 ● 5.8 = 29 left side 6.3 ● 5.8 = 36.54 right side 6.3 ● 5.8 = 36.54 two bases Add to find the total surface area. 29 + 36.54 + 36.54 + 29 = 131.08 Answer: The surface area of the tent is about 131.1 square feet. Lesson 7 Ex2

DECORATING Julia is painting triangular prisms to use as decoration in her garden. Find the surface area of the prism. A. 85.5 in2 B. 90.2 in2 C. 93.1 in2 D. 108.4 in2 A B C D Lesson 7 CYP2

Lesson 7 Key Concept 2

Surface Areas of Cylinders Find the lateral area and the surface area of the cylinder. Round to the nearest tenth. Lateral Surface Area Total Surface Area Answer: The lateral surface area is about 31.4 square meters, and the total surface area is about 70.7 square meters. Lesson 7 Ex3

Find the total surface area of the cylinder. Round to the nearest tenth. A. 176.4 mm2 B. 188.7 mm2 C. 207.3 mm2 D. 245.1 mm2 A B C D Lesson 7 CYP3

Surface Areas of Cylinders LABELS Find the area of the label on the can of juice. Round to the nearest tenth. Since the label covers the lateral surface of the can, you only need to find the can’s lateral surface area. Lesson 7 Ex4

Surface Areas of Cylinders Estimate 113.1 Answer: The area of the label is about 113.1 square inches. Lesson 7 Ex4

LABELS Find the area of the label on the can of juice LABELS Find the area of the label on the can of juice. Round to the nearest tenth. A. 132.9 in2 B. 155.5 in2 C. 164.4 in2 D. 185.2 in2 A B C D Lesson 7 CYP4

End of Lesson 7

Five-Minute Check (over Lesson 7-7) Main Idea and Vocabulary Targeted TEKS Key Concepts: Lateral Surface Area of a Pyramid Example 1: Surface Areas of a Pyramid Example 2: Real-World Example Lesson 8 Menu

Find the lateral and total surface areas of pyramids. Regular pyramid Pyramid whose base is a regular polygon slant height AKA the “Lateral height” The height of a FACE of a pyramid. This height goes down the SIDE of a pyramid DIFFERENT than the ACTUAL height of the pyramid!!! Lesson 8 MI/Vocab

Still 3 ways to solve Surface Area problems NOTES Still 3 ways to solve Surface Area problems Nets Sides – Add areas of all sides Formulas Lateral Surface Area = ½ Pl P = PERIMETER of base l = LATERAL height, NOT actual height Total SA = L + B or ½ Pl + B B = Area of the base BE CAREFUL ON THE HEIGHT!! May have to use Pythagorean Theorem to find lateral height!! Lesson 8 TEKS

Lesson 8 Key Concept 1

Surface Areas of a Pyramid Find the lateral and total surface areas of the triangular pyramid. Find the lateral area and the area of the base. Area of each lateral face Area of a triangle Replace b with 5 and h with 8. Lesson 8 Ex1

Surface Areas of a Pyramid There are 3 faces, so the lateral area is 3(20) or 60 square inches. Area of base A = 10.8 in2 Answer: The lateral surface area of the pyramid is 60 square inches. The total surface area is 60 + 10.8 or 70.8 square inches. Lesson 8 Ex1

Find the total surface area of the square pyramid. A. 156 cm2 B. 174 cm2 C. 182 cm2 D. 204 cm2 A B C D Lesson 8 CYP1

Lateral surface area of a pyramid TOYS A toy block has the shape of a regular pyramid with a square base. The manufacturer wants to paint the lateral surface green. How many square centimeters will be painted green? Lateral surface area of a pyramid P = 7(4) or 28 and = 8 Simplify. Answer: The lateral surface area is 112 square centimeters. Lesson 8 Ex2

TOYS A toy block has the shape of a regular pyramid with a square base TOYS A toy block has the shape of a regular pyramid with a square base. The manufacturer wants to paint the lateral surface green. How many square centimeters will be painted green? A. 175 cm2 B. 210 cm2 C. 235 cm2 D. 260 cm2 A B C D Lesson 8 CYP2

End of Lesson 8

Five-Minute Check (over Lesson 7-8) Main Idea and Vocabulary Targeted TEKS Example 1: Find Missing Linear Measures Key Concepts: Ratios of Similar Solids Example 2: Find Surface Area of a Similar Solid Example 3: Find Volume of a Similar Solid Lesson 9 Menu

Find dimensions, surface area, and volume of similar solids. Same shape LINEAR measurements are proportional AREAS AND VOLUME ARE NOT THE SAME PROPORTION AS THE SIDES!! Lesson 9 MI/Vocab

If 2 Polygons are Similar they have 4 things in common: They have the SAME shape They have the SAME angles They have a SCALE FACTOR between them THEIR SIDES ARE PROPORTIONAL!!!! If the sides are proportional, then their perimeters are proportional as well. The “Scale Factor” is “How much bigger or smaller” one shape is than another. Scale Factor = NEW OLD Lesson 5 TEKS

NOTES – Two ways to solve similar solid problems Just like with similar figures, you can use proportions to find missing measures Same measurements on top and same measurements on bottom. Measurement sides must be raised to an exponent Area = SQUARED Volume = CUBED Lesson 9 TEKS

AREA Scale Factor = (ACTUAL Scale Factor)2 NOTES – Two ways to solve similar solid problems 2) Use Dilation equation to find new AREA and VOLUME Original * Scale Factor = New AREA Scale Factor = (ACTUAL Scale Factor)2 Volume Scale Factor = (ACTUAL Scale Factor)3 Lesson 9 TEKS

Find Missing Linear Measures These cones are similar. What is the radius of Cone A to the nearest tenth? Since the two cones are similar, the ratios of their corresponding linear measures are proportional. Words Variable Equation Lesson 9 Ex1

Find Missing Linear Measures Write the proportion. Find the cross products. Multiply. Divide each side by 12. Simplify. Answer: The radius of cone A is about 4.7 centimeters. Lesson 9 Ex1

Cone A Cone B The cones are similar. What is the radius of Cone B to the nearest tenth? A. 6.5 cm B. 7.0 cm C. 7.5 cm D. 8.0 cm A B C D Lesson 9 CYP1

Lesson 9 Key Concept 1

Find Surface Area of a Similar Solid These rectangular prisms are similar. Find the total surface area of Prism A. The ratio of the measures of prism A to prism B is Lesson 9 Ex2

Find Surface Area of a Similar Solid Write a proportion. Substitute the known values. Let S represent the surface area. Simplify. Find the cross products. Divide each side by 4. Simplify. Answer: The surface area of prism A is 846 square inches. Lesson 9 Ex2

These square pyramids are similar These square pyramids are similar. Find the total surface area of Pyramid A. A. 476 cm2 B. 528 cm2 C. 562 cm2 D. 640 cm2 A B C D Lesson 9 CYP2

Find Volume of a Similar Solid A triangular prism has a volume of 12 cm3. Suppose the dimensions are tripled. What is the volume of the new prism? A. 36 cm3 B. 96 cm3 C. 324 cm3 D. 1,728 cm3 Read the Test Item Lesson 9 Ex3

Find Volume of a Similar Solid Solve the Test Item Lesson 9 Ex3

Find Volume of a Similar Solid Write a proportion. Substitute the known values. Let V represent the volume of the larger prism. Simplify. Find the cross products. Simplify. Answer: So, the volume of larger prism is 324 cubic centimeters. The answer is C. Lesson 9 Ex3

A hexagonal prism has a volume of 25 cubic inches A hexagonal prism has a volume of 25 cubic inches. Suppose the dimensions are tripled. What is the volume of the new prism? A. 75 in3 B. 120 in3 C. 200 in3 D. 675 in3 A B C D Lesson 9 CYP3

End of Lesson 9

Five-Minute Checks Image Bank Math Tools Animation Menu Surface Area of Prisms CR Menu

Lesson 7-1 (over Chapter 6) Lesson 7-2 (over Lesson 7-1) 5Min Menu

1. Exit this presentation. To use the images that are on the following three slides in your own presentation: 1. Exit this presentation. 2. Open a chapter presentation using a full installation of Microsoft® PowerPoint® in editing mode and scroll to the Image Bank slides. 3. Select an image, copy it, and paste it into your presentation. IB 1

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7-6 Volume of Pyramids, Cones, and Spheres 7-8 Making a Pyramid Animation Menu

Animation 1

Animation 2

Refer to the figure. Find m1 if m2 is 35°. (over Chapter 6) Refer to the figure. Find m1 if m2 is 35°. A. 145° B. 125° C. 55° D. 35° A B C D 5Min 1-1

(over Chapter 6) Find the coordinates of the vertices of triangle LMN with vertices L(2, –1), M(0, –3), and N(4, –3) translated by (–2, 3). A. L'(0, 2), M'(–2, 0), N'(2, 0) B. L'(0, 4), M'(–2, 0), N'(2, 0) C. L'(4, 2), M'(2, 0), N'(6, 0) D. L'(4, –4), M'(2, –6), N'(6, –6) A B C D 5Min 1-2

(over Chapter 6) Find the coordinates of the vertices of rectangle JKLM with vertices J(–5, 4), K(–2, 4), L(–2, 3), and M(–5, 3) translated by (1, –2). A. J'(–4, 2), K'(–1, 2), L'(–1, 1), M'(6, 1) B. J'(–4, 2), K'(3, 2), L'(–1, 1), M'(–4, 1) C. J'(–4, 2), K'(–1, 2), L'(–1, 1), M'(–4, 1) D. J'(6, 2), K'(–1, 2), L'(–1, 1), M'(–4, 1) A B C D 5Min 1-3

(over Chapter 6) Find the coordinates of the vertices of trapezoid PQRS with vertices P(–4, –3), Q(–1, –3), R(–1, –2), and S(–4, –1) translated by (5, 1). A. P'(1, –2), Q'(4, –2), R'(4, –1), S'(1, 2) B. P'(1, –2), Q'(4, –2), R'(4, –1), S'(1, 0) C. P'(1,4), Q'(4, –2), R'(4, –1), S'(1, 0) D. P'(1, –2), Q'(4, 4), R'(4, –1), S'(1, 0) A B C D 5Min 1-4

Refer to the figure. What is the measure of angle C? (over Chapter 6) Refer to the figure. What is the measure of angle C? A. 40° B. 80° C. 100° D. 140° A B C D 5Min 1-5

(over Lesson 7-1) Find the circumference and area of the circle in the figure. Round to the nearest tenth. A. 34.5 m; 121 m2 B. 34.5 m; 380.1 m2 C. 69.1 m; 190.1 m2 D. 69.1 m; 380.1 m2 A B C D 5Min 2-1

(over Lesson 7-1) Find the circumference and area of the circle in the figure. Round to the nearest tenth. A. 16.5 ft; 86.6 ft2 B. 33.0 ft; 86.6 ft2 C. 16.5 ft; 33.0 ft2 D. 33.0 ft; 43.3 ft2 A B C D 5Min 2-2

(over Lesson 7-1) Find the circumference and area of the circle in the figure. Round to the nearest tenth. A. 157.1 yd; 1963.5 yd2 B. 157 yd; 490.9 yd2 C. 78.5 yd; 490.9 yd2 D. 78.5 yd; 245.3 yd2 A B C D 5Min 2-3

(over Lesson 7-1) Find the circumference and area of the circle in the figure. Round to the nearest tenth. A. 14.1 in.; 15.9 in2 B. 15.9 in.; 63.6 in2 C. 14.1 in.; 63.6 in2 D. 28.3 in.; 63.6 in2 A B C D 5Min 2-4

(over Lesson 7-1) Find the circumference and area of a circle that has a radius of 13 miles. Round to the nearest tenth. A. 40.8 mi; 265.4 mi2 B. 40.8 mi; 530.9 mi2 C. 81.7 mi; 265.4 mi2 D. 81.7 mi; 530.9 mi2 A B C D 5Min 2-5

(over Lesson 7-1) Find the area of a circle whose diameter is 7 cm. Round to the nearest tenth. A. 23.2 cm2 B. 36.3 cm2 C. 43.0 cm2 D. 82.6 cm2 A B C D 5Min 2-6

(over Lesson 7-2) Minnesota is known as the "Land of 10,000 Lakes." The total area of Minnesota is 86,943 square miles. Of that, about 8.4% of the area is water. About how many square miles of Minnesota's area is not covered by water? Round your answer to the nearest tenth. Use the solve a simpler problem strategy. A. 7,303.2 square miles B. 94,246.2 square miles C. 79,639.8 square miles D. 36,743.8 square miles A B C D 5Min 3-1

A. 8 packages of 4; 7 packages of 7 (over Lesson 7-2) Natasha is giving each of her 27 classmates 3 pieces of chocolate as a treat for her birthday. If the chocolates are sold in packages of 4 and 7, how many of each size package should she buy? Use the solve a simpler problem strategy. A. 8 packages of 4; 7 packages of 7 B. 4 packages of 4; 14 packages of 7 C. 5 packages of 4; 8 packages of 7 D. 11 packages of 4; 6 packages of 7 A B C D 5Min 3-2

(over Lesson 7-2) 650 customers of a restaurant were surveyed. If 30% of the customers voted for a new dessert to be added to the menu, find the number of customers who voted against adding the new dessert to the menu. Use the solve a simpler problem strategy. A. 845 customers B. 455 customers C. 90 customers D. 65 customers A B C D 5Min 3-3

(over Lesson 7-2) The length of a $10 roll of a tightly wrapped roll of quarters is 70 mm. About how wide is one quarter? Use the solve a simpler problem strategy. A. 3.5 mm B. 2.33 mm C. 1.75 mm D. 1.50 mm A B C D 5Min 3-4

(over Lesson 7-3) Find the area of the figure shown. Round to the nearest tenth if necessary. A. 18 cm2 B. 27 cm2 C. 36 cm2 D. 45 cm2 A B C D 5Min 4-1

(over Lesson 7-3) Find the area of the figure shown. Round to the nearest tenth if necessary. A. 25 mi2 B. 36 mi2 C. 67 mi2 D. 74 mi2 A B C D 5Min 4-2

(over Lesson 7-3) What is the area of the figure shown in the picture? Round to the nearest tenth if necessary. A. 80.5 in2 B. 85.7 in2 C. 161.0 in2 D. 105.0 in2 A B C D 5Min 4-3

A. cube; 6 faces, all squares; 12 edges; 8 vertices (over Lesson 7-4) Identify the solid shown. Name the number and shapes of the faces. Then name the number of edges and vertices. A. cube; 6 faces, all squares; 12 edges; 8 vertices B. cube; 4 faces, all squares; 12 edges; 8 vertices C. cube; 4 faces, all squares; 8 edges; 12 vertices D. cube; 6 faces, all squares; 8 edges; 12 vertices A B C D 5Min 5-1

A. rectangular prism; 4 faces, all rectangles; 12 edges; 8 vertices (over Lesson 7-4) Identify the solid shown. Name the number and shapes of the faces. Then name the number of edges and vertices. A. rectangular prism; 4 faces, all rectangles; 12 edges; 8 vertices B. rectangular prism; 4 faces, all rectangles; 8 edges; 12 vertices C. rectangular prism; 6 faces, all rectangles; 12 edges; 8 vertices D. rectangular prism; 6 faces, all rectangles; 8 edges; 12 vertices A B C D 5Min 5-2

(over Lesson 7-4) Determine whether the statement is sometimes, always, or never true. Explain your reasoning. A pyramid has at least four vertices. A. Always; the smallest number of vertices on the base is 3 for a triangular pyramid plus the fourth vertex where the lateral faces meet. B. Sometimes; the smallest number of vertices is 3 for a triangular pyramid. Only some pyramids have a fourth vertex where the lateral faces meet. C. Never; the largest number of vertices for a pyramid is 3. A B C 5Min 5-3

A. Always; polyhedrons have only curved edges. (over Lesson 7-4) Determine whether the statement is sometimes, always, or never true. Explain your reasoning. The edge of a polyhedron can be a circle. A. Always; polyhedrons have only curved edges. B. Sometimes; some polyhedrons have line segments for edges. C. Never; polyhedrons have only line segments for edges. A B C 5Min 5-4

Which of the following is represented by a point? (over Lesson 7-4) Which of the following is represented by a point? A. face B. vertex C. base D. edge A B C D 5Min 5-6

(over Lesson 7-5) Find the volume of the given solid. Round to the nearest tenth if necessary. A. 254.8 in3 B. 382.2 in3 C. 441.6 in3 D. 764.5 in3 A B C D 5Min 6-1

(over Lesson 7-5) Find the volume of the given solid. Round to the nearest tenth if necessary. A. 25.5 cm3 B. 51 cm3 C. 76.5 cm3 D. 153 cm3 A B C D 5Min 6-2

(over Lesson 7-5) Find the volume of the given solid. Round to the nearest tenth if necessary. A. 91.1 ft3 B. 45.6 ft3 C. 20.1 ft3 D. 13.5 ft3 A B C D 5Min 6-3

(over Lesson 7-5) The base of the triangle of a triangular prism is 3 yd, the altitude is 5 yd, and the height is 9 yd. Find the volume of the triangular prism. Round to the nearest tenth if necessary. A. yd3 B. yd3 C. yd3 D. yd3 A B C D 5Min 6-4

(over Lesson 7-5) Find the volume of a rectangular prism if the length is 4.6 m, width is 8.2 m, and height is 5.3 m. Round to the nearest tenth if necessary. A. 199.9 m3 B. 99.9 m3 C. 67.8 m3 D. 33.9 m3 A B C D 5Min 6-5

(over Lesson 7-5) The volume of a rectangular prism is 440 mm3. If the length is 8 mm and the height is 5 mm, what is the width? A. 4 mm B. 9 mm C. 10 mm D. 11 mm A B C D 5Min 6-6

(over Lesson 7-6) Find the volume of the given solid. Round to the nearest tenth if necessary. A. 15 m3 B. 20 m3 C. 40 m3 D. 60 m3 A B C D 5Min 7-1

(over Lesson 7-6) Find the volume of the given solid. Round to the nearest tenth if necessary. A. 1,026.3 ft3 B. 1,539.1 ft3 C. 2,931.6 ft3 D. 3,078.2 ft3 A B C D 5Min 7-2

(over Lesson 7-6) Find the volume of the given solid. Round to the nearest tenth if necessary. A. 35 cm3 B. 50 cm3 C. 70 cm3 D. 105 cm3 A B C D 5Min 7-3

(over Lesson 7-6) Find the volume of a sphere with radius 6 in. Round to the nearest tenth if necessary. A. 37.7 in3 B. 226.2 in3 C. 150.8 in3 D. 904.8 in3 A B C D 5Min 7-4

(over Lesson 7-6) Find the volume of a triangular pyramid if the triangle base has base 6.5 yd and height 2.25 yd, and the prism height is 5.75 yd. Round to the nearest tenth if necessary. A. 14.0 yd3 B. 28.0 yd3 C. 42.0 yd3 D. 84.0 yd3 A B C D 5Min 7-5

(over Lesson 7-6) Ricky bought a box of ice cream cones. Ricky wants to know how much ice cream each cone can hold. If each cone has a diameter of 3 inches and a height of 5 inches, what is the approximate volume of each cone? A. 7.9 in3 B. 11.8 in3 C. 35.3 in3 D. 39.3 in3 A B C D 5Min 7-6

(over Lesson 7-7) Find the surface area of the given solid. Round to the nearest tenth if necessary. A. 257.6 yd2 B. 229.3 yd2 C. 116.2 yd2 D. 58.1 yd2 A B C D 5Min 8-1

(over Lesson 7-7) Find the surface area of the given solid. Round to the nearest tenth if necessary. A. 108 ft2 B. 114 ft2 C. 120 ft2 D. 132 ft2 A B C D 5Min 8-2

(over Lesson 7-7) Find the surface area of the given solid. Round to the nearest tenth if necessary. A. 1,442.9 m2 B. 752.6 m2 C. 501.8 m2 D. 201.6 m2 A B C D 5Min 8-3

(over Lesson 7-7) Find the surface area of a cylinder having diameter 14.5 in. and height 6.25 in. Round to the nearest tenth if necessary. A. 615.0 in2 B. 1032.1 in2 C. 1890.5 in2 D. 2075.1 in2 A B C D 5Min 8-4

(over Lesson 7-7) Find the surface area of a rectangular prism with length 20 cm, width 3 cm, and height 2 cm. Round to the nearest tenth if necessary. A. 50 cm2 B. 106 cm2 C. 120 cm2 D. 212 cm2 A B C D 5Min 8-5

(over Lesson 7-7) Jeffrey bought his father a can of tennis balls for his birthday. Jeffrey wants to wrap the can in wrapping paper. If the can has a height of 8.5 inches and a radius of 1.5 inches, how much wrapping paper will Jeffrey need? A. 62.8 in2 B. 89.5 in2 C. 94.2 in2 D. 129.6 in2 A B C D 5Min 8-6

(over Lesson 7-8) Find the surface area of the given solid. Round to the nearest tenth if necessary. A. 25.1 ft2 B. 48.4 ft2 C. 50.3 ft2 D. 100.5 ft2 A B C D 5Min 9-1

(over Lesson 7-8) Find the surface area of the given solid. Round to the nearest tenth if necessary. A. 281.6 cm2 B. 238.3 cm2 C. 195 cm2 D. 140.8 cm2 A B C D 5Min 9-2

(over Lesson 7-8) Find the surface area of the given solid. Round to the nearest tenth if necessary. A. 64 yd2 B. 112 yd2 C. 176 yd2 D. 448 yd2 A B C D 5Min 9-3

(over Lesson 7-8) Find the surface area of a cone with diameter 7 feet and slant height 4 feet. Round to the nearest tenth if necessary. A. 55.2 ft2 B. 88.0 ft2 C. 173.2 ft2 D. 346.3 ft2 A B C D 5Min 9-4

(over Lesson 7-8) The base of a conical building has a circumference of 20 meters. The slant height of the building is 30 feet. What is the best estimate of the lateral area of the building? A. 7 m2 B. 100 m2 C. 300 m2 D. 1,800 m2 A B C D 5Min 9-5

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