Vocabulary. Term Page Definition Clarifying Example. cone. cube. cylinder. edge of a threedimensional. figure. face of a polyhedron.

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1 CHAPTER 10 Vocabulary The table contains important vocabulary terms from Chapter 10. As you work through the chapter, fill in the page number, definition, and a clarifying example. cone Term Page Definition Clarifying Example cube cylinder edge of a threedimensional figure face of a polyhedron isometric drawing orthographic drawing 208 Geometry

2 CHAPTER 10 Vocabulary The table contains important vocabulary terms from Chapter 10. As you work through the chapter, fill in the page number, definition, and a clarifying example. Term Page Definition Clarifying Example cone 654 A three-dimensional figure with a circular base and a curved lateral surface that connects the base to a point called the vertex. cube 654 A prism with six square faces. cylinder 654 A three-dimensional figure with two parallel circular bases and a curved lateral surface that connects the bases. edge of a threedimensional figure 654 A segment that is the intersection of two faces of the figure. edge face of a polyhedron 654 A flat surface of the polyhedron. face isometric drawing 662 A way of drawing threedimensional figures using isometric dot paper, which has equally spaced dots in a repeating triangular pattern. orthographic drawing 661 A drawing that shows a three-dimensional object in which the line of sight for each view is perpendicular to the plane of the picture. Left Front Top Bottom Back Right 208 Geometry

3 CHAPTER 10 VOCABULARY CONTINUED Term Page Definition Clarifying Example perspective drawing polyhedron prism pyramid sphere surface area vanishing point volume 209 Geometry

4 CHAPTER 10 VOCABULARY CONTINUED Term Page Definition Clarifying Example perspective drawing 662 A drawing in which nonvertical parallel lines meet at a point called a vanishing point. Perspective drawings can have one or two vanishing points. Vanishing point Horizon polyhedron 670 A closed three-dimensional figure formed by four or more polygons that intersect only at their edges. prism 654 A polyhedron formed by two parallel congruent polygonal bases connected by lateral faces that are parallelograms. pyramid 654 A polyhedron formed by a polygonal base and triangular lateral faces that meet at a common vertex. sphere 714 The set of points in space that are a fixed distance from a given point called the center of the sphere. center surface area 680 The total area of all faces and curved surfaces of a three-dimensional figure. 12 cm Surface 6 cm area = 8 cm 2(8)(12) + 2(8)(6) + 2(12)(6) = 432 cm 2 vanishing point 662 In a perspective drawing, a point on the horizon where parallel lines appear to meet. volume 697 The number of nonoverlapping unit cubes of a given size that will exactly fill the interior of a three-dimensional figure. 4 ft 3 ft 12 ft Volume = (3)(4)(12) = 144 ft Geometry

5 CHAPTER 10 Chapter Review 10-1 Solid Geometry Classify each figure. Name the vertices, edges and bases R 3. L G M T S H U Describe the three-dimensional figure that can be made from the given net Geometry

6 CHAPTER 10 Chapter Review 10-1 Solid Geometry Classify each figure. Name the vertices, edges and bases R 3. L G M T S H U Cylinder : vertices: none, edges: none, bases: L and M Triangular pyramid: vertices: R, S, T, U edges: RS, SU, RU, RT, TU, ST bases: triangle STU. Cone: vertices G, edges: none, bases: H Describe the three-dimensional figure that can be made from the given net The net has two congruent triangular faces. The remaining faces are rectangles, so the net forms a triangular prism. The net has one circle and a circle with a pie piece missing. This net forms a cone. The net has six congruent rectangles. The remaining faces are 2 hexagons, so the net forms a hexagonal prism. 225 Geometry

7 Describe the cross section Representations of Three-Dimensional Figures Use the figure made of unit cube for Problems 10 and 11. Assume there are no hidden cubes. 10. Draw all six orthographic views. 11. Draw an isometric view. 226 Geometry

8 Describe the cross section Circle Triangle Hexagon 10-2 Representations of Three-Dimensional Figures Use the figure made of unit cube for Problems 10 and 11. Assume there are no hidden cubes. 10. Draw all six orthographic views. top right side left side bottom front back 11. Draw an isometric view. 226 Geometry

9 12. Draw the block letter F in one-point perspective. 13. Draw the block letter F in two-point perspective Formulas in Three Dimensions Find the number of vertices, edges, and faces of each polyhedron. Use your results to verify the Euler s formula. 14. rectangular prism 15. pentagonal pyramid 16. rectangular pyramid 17. A fish tank is in the shape of a rectangular prism. The base of the fish tank is 2 ft by 3 ft and has a 4.5 ft diagonal. What is the height of the fish tank? 227 Geometry

10 12. Draw the block letter F in one-point perspective. 13. Draw the block letter F in two-point perspective Formulas in Three Dimensions Find the number of vertices, edges, and faces of each polyhedron. Use your results to verify the Euler s formula. 14. rectangular prism 15. pentagonal pyramid 16. rectangular pyramid vertices: 8, edges: 12, faces: 6 V E F vertices: 6, edges: 10, faces: 6 V E F vertices: 5, edges: 8, faces: 5 V E F A fish tank is in the shape of a rectangular prism. The base of the fish tank is 2 ft by 3 ft and has a 4.5 ft diagonal. What is the height of the fish tank? 2.7 ft 227 Geometry

11 Find the distance between the given points. Find the midpoint of the segments with the given end points. Round to the nearest tenth, if necessary. 18. (0, 0, 0) and 19. (4, 1, 1) and 20. (5, 6, 2) and (6, 8, 12) (3, 3, 5) (4, 2, 6) 10-4 Surface Area of Prisms and Cylinders Find the surface area of each figure. Round to the nearest tenth, if necessary in in. 24 in. 6 ft 5 in. 30 in. 4 ft 6 in. 4 in. 24. The dimensions of a 12 in. by 9 in. by 24 in. right rectangular prism are multiplied by 2. Describe the affect on the surface area Surface Area of Pyramids and Cones Find the surface area of each figure. Round to the nearest tenth, if necessary. 25. a regular square pyramid with 26. a right cone with diameter 32 cm base edge length of 6 ft and and height 18 cm slant height 14 ft 228 Geometry

12 Find the distance between the given points. Find the midpoint of the segments with the given end points. Round to the nearest tenth, if necessary. 18. (0, 0, 0) and 19. (4, 1, 1) and 20. (5, 6, 2) and (6, 8, 12) (3, 3, 5) (4, 2, 6) distance 15.6 units; midpoint M (3, 4, 6) distance 7.3 units; midpoint M (3.5, 1, 2) distance 11.4 units; midpoint M (4.5, 2, 2) 10-4 Surface Area of Prisms and Cylinders Find the surface area of each figure. Round to the nearest tenth, if necessary in in. 24 in. 6 ft 5 in. 30 in. 4 ft 6 in. 4 in. SA 1980 in. 2 SA ft in The dimensions of a 12 in. by 9 in. by 24 in. right rectangular prism are multiplied by 2. Describe the affect on the surface area. 3 Answers may vary: The surface area will be 4 9 of the original surface area Surface Area of Pyramids and Cones Find the surface area of each figure. Round to the nearest tenth, if necessary. 25. a regular square pyramid with 26. a right cone with diameter 32 cm base edge length of 6 ft and and height 18 cm slant height 14 ft 204 ft cm Geometry

13 27. the composite figure formed by a cone and a cylinder 10 cm 5 cm 4 cm 10-6 Volume of Prisms and Cylinders Find the volume of each figure. Round to the nearest tenth if necessary. 28. a regular hexagonal prism with 29. a cylinder with radius 3 yd and base area 192 in. 2 and height height 11 yd 24 in. 30. A brick patio measures 8 ft by 10 ft by 3 in. Find the volume of the bricks. If the density of a brick is about 140 pounds per cubic foot, what is the weight of the patio in pounds? 31. The dimensions of a cylinder with diameter 2 ft and height 1 ft are reduced by half. Describe the affect on the volume Volume of Pyramids and Cones Find the volume of each figure. Round to the nearest tenth, if necessary m m 18 m 25 in. 9 in. 9 in. 6 m 8 m 8 m 229 Geometry

14 27. the composite figure formed by a cone and a cylinder 10 cm S (cone lateral area) (cylinder lateral area) (base area) S S 42.5 cm 2 4 cm 5 cm 10-6 Volume of Prisms and Cylinders Find the volume of each figure. Round to the nearest tenth if necessary. 28. a regular hexagonal prism with 29. a cylinder with radius 3 yd and base area 192 in. 2 and height height 11 yd 24 in yd in A brick patio measures 8 ft by 10 ft by 3 in. Find the volume of the bricks. If the density of a brick is about 140 pounds per cubic foot, what is the weight of the patio in pounds? 20 ft 3 ; 2800 pounds 31. The dimensions of a cylinder with diameter 2 ft and height 1 ft are reduced by half. Describe the affect on the volume. The volume will be 1 8 the original volume Volume of Pyramids and Cones Find the volume of each figure. Round to the nearest tenth, if necessary m m 18 m 25 in. 9 in. 9 in. 6 m 8 m 8 m V m 3 V 675 in. 3 V 768 m Geometry

15 10-8 Spheres Find the surface area and the volume of each figure. 35. a sphere with diameter 6 in. 36. a hemisphere with radius 5 cm 37. A playground ball has a diameter of about 9 in. A bouncy ball has the diameter of 3 in. About how many more times as great is the volume of the playground ball as the volume of a bouncy ball? 230 Geometry

16 10-8 Spheres Find the surface area and the volume of each figure. 35. a sphere with diameter 6 in. 36. a hemisphere with radius 5 cm SA 113 in. 2, V 113 in. 3 SA 157 cm 2, V 262 cm A playground ball has a diameter of about 9 in. A bouncy ball has the diameter of 3 in. About how many more times as great is the volume of the playground ball as the volume of a bouncy ball? The volume of the playground ball is about 27 times larger than that of the bouncy ball. 230 Geometry

17 CHAPTER 10 Big Ideas Answer these questions to summarize the important concepts from Chapter 10 in your own words. 1. Name the six different views of an object in an orthographic drawing. 2. Describe how you can find the distance between two points (x 1, y 1, z 1 ) and (x 2, y 2, z 2 ). 3. Describe the difference between surface area and lateral area. 4. Describe how the volume of a cone is related to the volume of a cylinder. For more review of Chapter 10: Complete the Chapter 10 Study Guide and Review on pages of your textbook. Complete the Ready to Go On quizzes on pages 679 and 725 of your textbook. 231 Geometry

18 CHAPTER 10 Big Ideas Answer these questions to summarize the important concepts from Chapter 10 in your own words. 1. Name the six different views of an object in an orthographic drawing. Top, bottom, front, back, left side and right side. 2. Describe how you can find the distance between two points (x 1, y 1, z 1 ) and (x 2, y 2, z 2 ). Answers may vary. The distance between the two points can be found by drawing a rectangular prism with the given points as endpoints of a diagonal. The formula for length of a diagonal can then be used. 3. Describe the difference between surface area and lateral area. Answers may vary. Surface area is the total of all the faces and curved surfaces of a three-dimensional figure. The lateral area of a prism is the sum of the areas of the lateral faces. 4. Describe how the volume of a cone is related to the volume of a cylinder. Answers may vary. The volume of a cone is one-third the volume of a cylinder. For more review of Chapter 10: Complete the Chapter 10 Study Guide and Review on pages of your textbook. Complete the Ready to Go On quizzes on pages 679 and 725 of your textbook. 231 Geometry