Assignment Guide: Chapter 11 Geometry (L3) (136) 11.1 Space Figures and Cross Sections Page 692-693 #7-23 odd, 35 (137) 11.2/11.4 Surface Areas and Volumes of Prisms Page 703-705 #1, 2, 7-9, 11-13, 25, 30 Page 721-723 #6-12, 19, 21, 24, 25, 33 (138) 11.2/11.4 Surface Areas and Volumes of Cylinders Page 703-705 #3, 4, 14-20, 26, 29 Page 721-723 #14-17, 23, 26, 32, 34, 37 (139) 11.6 Surface Areas and Volumes of Spheres Page 737-738 #7-21 odd, 23-25, 35-41 odd (140) Review: 11.1, 11.2, 11.4, 11.6 Worksheets (in assignment guide, pages 10-11) Study for quiz (11.1, 11.2, 11.4, 11.6) (141) Quiz: Sections 11.1, 11.2, 11.4, 11.6 Page 707 #53-55 and Page 724 #52-53 (142) 11.3/11.5 Surface Areas and Volumes of Pyramids Page 713-714 #9-14, 29, 34-36 and Page 729-730 #5-14 (143) 11.3/11.5 Surface Areas and Volumes of Cones Page 713-714 #16-21, 23, 30 Page 730-731 #15-19, 29, 31 (144) 11.7 Areas and Volumes of Similar Solids Page 746-749 #5-23 odd, 24, 30-37, 40-41 (145) Review: 11.3, 11.5, 11.7 Worksheets (in assignment guide, page 18) Study for quiz (11.3, 11.5, 11.7) (146) Quiz: Sections 11.3, 11.5, 11.7 Worksheets (in assignment guide, pages 19-20) (147) Review: Chapter 11 Page 755 #1-19 Study for Test (Chapter 11) (148) TEST: Chapter 11 Page 759 #1-15 This is a guide. Homework is subject to change. Check the chalkboard in class for updates and/or changes.
Geometry Notes, Section 11.1 Space Figures and Cross Sections Polyhedron: Three-dimensional figure with that are polygons. intersect at, and meet at. Euler s Formula: (polyhedron) Euler s Formula: (net) Relates faces, vertices, and edges of a polyhedron. + = + Relates faces, vertices, and edges of a polyhedron net. + = + Try this: What does a net for the doorstop at the right look like? Label the net with its appropriate dimensions. Verify both versions of Euler s Formula. Draw a net for each three-dimensional figure. Verify both versions of Euler s Formula. 1
Geometry Notes, Section 11.1 (continued) Cross-Section: The intersection of a and a. These can be many different shapes, including circles. Example: The cross section of this solid and this plane is a rectangle. This cross section is a horizontal plane. To draw a cross section: Visualize a plane intersecting one face at a time in parallel segments. Draw the parallel segments, joining their endpoints. Shade the cross section. Try these: Draw and describe the cross section formed by intersecting the rectangular prism with the plane described. 3. A plane that contains the horizontal line of symmetry 4. A plane that passes through the midpoint of the top left edge, the midpoint of the top front edge, and the midpoint of the left front edge 5. What is the cross section formed by a plane that contains a vertical line of symmetry for the figure at the right? 2
Geometry Practice, Section 11.1 Space Figures and Cross Sections For each polyhedron, how many faces, edges, and vertices are there? Verify Euler s Formula. 1. F = 2. F = 3. F = E = E = E = V = V = V = Draw a net for each polyhedron. Verify Euler s Formula for the nets. 4. 2. 3. Use Euler s Formula to fill in the missing values for each polyhedron. Faces Edges Vertices Faces Edges Vertices 4. 12 8 5. 24 16 6. 9 14 7. 8 6 Describe each cross-section. 10. 11. 12. 3
Geometry Notes, Sections 11.2/11.4 Surface Area and Volume of Prisms Prism: A polyhedron with two congruent parallel faces called. The non-base faces of a prism are. Lateral Area LA ph p = perimeter of the base h = height of the prism Surface Area SA LA 2B LA = lateral area of the prism B = area of the base Volume: V Bh B = area of the base h = height of the prism Try these: Find the lateral area, surface area, and volume of each figure below. 3. 4. (Find the volume only.) 4
Geometry Practice, Sections 11.2/11.4 Surface Area and Volume of Prisms Find the lateral area, surface area, and volume of each figure below. 3. 4. Find the volume. Find the value of x, to the nearest integer. 5 6. Volume: 576 cm 3 5
Geometry Notes, Sections 11.2/11.4 Surface Area and Volume of Cylinders Cylinder: A three-dimensional figure with two congruent bases. Lateral Area LA Ch C = circumference of the base h = height of the cylinder Surface Area SA LA 2B LA = lateral area B = area of the circle ( r 2 ) Volume: V Bh B = area of the circle ( r 2 ) h = height of the cylinder Try these: Find the lateral area, surface area, and volume of each figure below. 3. 4. (Find the volume only.) 6
Geometry Practice, Sections 11.2/11.4 Surface Area and Volume of Cylinders Find the lateral area, surface area, and volume of each figure below. 3. 4. Find the volume. Find the value of x, to the nearest integer. 5 6. Volume: 602.88 cm 3 7
Geometry Notes, Section 11.6 Surface Area and Volume of Spheres Sphere: The set of all points to a point called the. A segment that goes from the center to the edge of the sphere is a. A segment that goes from one side of the sphere to the other and passes through the center is a. Surface Area 2 SA 4 r r = radius of the circle Volume V 4 r 3 r = radius of the circle 3 Try these: Find the surface area and volume of each sphere below. 3. 4. A sphere has a surface area of 81 in. 2. What is its volume? 5. A sphere has a volume of 750 m 3. What is its surface area? 8
Geometry Practice, Section 11.6 Surface Area and Volume of Spheres Find the surface area and volume of each of the following spheres. Given the following volumes, find the surface area of each sphere. 3. V = 750 m 3 4. V = 4500 cm 3 Given the following surface areas, find the volume of each sphere. 5. SA = 81 in. 2 6. SA = 6084 m 2 Use the circumference given to find the surface area of each given object. 7. a bowling ball with C = 27 in. 8. a head of lettuce with C = 22 in. Find the radius of the sphere, given the ratio of the surface area (in square inches) to the volume (in cubic inches). 9. The ratio of the surface area in square inches to the volume in cubic inches is 4 : 1. 10. The ratio of the surface area in square feet to the volume in cubic feet is 2 : 5. 9
Geometry Review 11.1, 11.2, 11.4, 11.6: Surface Area and Volume of Prisms, Cylinders and Spheres Find the surface area and volume of each of the following figures. 3. 4. (Find the volume only.) 5. 6. 7. 8. 10
Describe the cross section formed in each diagram. 9. 10. 11. The volume of a sphere is 256 3 in 3. Find the surface area. 12. A cylinder has a height of 4 mm and a volume of 64 mm 3. What is the radius of the base? 13. The surface area of a sphere is 100. What is its volume? 14. Your friend draws a net of a prism. What is your friend s error? 15. The sphere at the right fits snugly inside a cube with 18 cm edges. What is the volume of the sphere? What is the surface area of the sphere? 11
Geometry Notes, Sections 11.3/11.5 Surface Area and Volume of Pyramids Pyramid: A polyhedron in which the base is, and the lateral faces are that meet at a. The height is the measure of the altitude of the. The slant height is the measure of the altitude of a. Lateral Area LA = ½pl Surface Area SA LA B Volume V = ⅓Bh p = perimeter of the base l = slant height of the pyramid LA = lateral area of the pyramid B = area of the base B = area of the base h = height of the pyramid Try these: Find the lateral area, surface area, and volume of each figure below. 3. 4. 12
Geometry Practice, Sections 11.3/11.5 Surface Area and Volume of Pyramids Find the lateral area, surface area, and volume of each figure below. 21 in. 3. 4. 5. 6. 120 m 2 4 m 13
Geometry Notes, Sections 11.3/11.5 Surface Area and Volume of Cones Cone: A three-dimensional figure like a pyramid, except the base is a. Lateral Area: 1 LA pl 2 Surface Area: SA LA B Volume: V = Bh p = perimeter of circular base l = lateral height of the cone LA = lateral area of the cone B = area of the circular base ( r 2 ) B = area of the circular base ( r 2 ) h = height of the cone *Note: You will need to use the Pythagorean Theorem Try these: Find the lateral area, surface area, and volume of each cone below. 3. 4. with radius 16 cm and slant height 20 cm 5. One right circular cone is set inside a larger right circular cone. Find the volume of the space between the cones if the diameter of the inside cone is 9 in., the diameter of the outside cone is 15 in., and the height of both is 8 in. 14
Geometry Practice, Sections 11.3/11.5 Surface Area and Volume of Cones Find the lateral area, surface area, and volume of each cone below. 3. 4. 5. A spherical scoop of ice cream with a diameter of 4 cm rests on top of a sugar cone that is 10 cm deep and has a diameter of 4 cm. If all of the ice cream melts into the cone, what percent of the cone will be filled? 6. The Pyramid of Khufu is a square pyramid which had a side length of about 230 m and a height of about 147 m when it was completed. The Pyramid of Khafre had a side length of about 215 m and a height of about 144 m when it was completed. What was the approximate difference in the volume of the two pyramids upon completion? 15
Geometry Notes, Section 11.7 Areas and Volumes of Similar Solids When two solids are similar, their corresponding dimensions are. This means we can set up proportions based on corresponding parts and the following formulas. Scale Factor (and Length) Area Volume a: b a : b 2 2 a : b 3 3 Example: The cubes shown at right are similar. Find the scale factor, the ratio of the surface areas, and the ratio of the volumes. Scale factor: 8 2 12 3 Ratio of Surface Areas: 2 2 4 2 3 9 Ratio of Volumes: 3 2 8 3 3 27 Try these: The surface areas (SA) of two similar figures are given. The volume of the larger figure is given. Find the volume of the smaller figure. 1. SA = 36 m 2 SA = 225 m 2 V = 750 m 3 2. SA = 108 in 2 SA = 192 in 2 V = 1408 in 3 3. SA= 49 m 2 SA= 441 m 2 V = 432 m 3 4. A shipping box holds 350 golf balls. A larger shipping box has dimensions triple the size of the other box. How many golf balls does the larger box hold? 5. A cylindrical thermos has a radius of 2 in. and is 5 in. high. It holds 10 f oz. To the nearest ounce, how many ounces will a similar thermos with a radius of 3 in. hold? 16
Geometry Practice, Section 11.7 Areas and Volumes of Similar Solids Are the given solids similar? 1. Two regular square pyramids have heights 10 and 12. The bases are squares with sides 4 and 4.8. 2. One rectangular solid has length 7, width 5, and height 3. Another rectangular solid has length 14, width 10, and height 10. 3. Two right triangular prisms have height 4 and 6. Their bases are triangles with sides 3, 4, 5 and 6, 8, 10. Complete the table. 4. 5. 6. 7. 8. scale factor 2:5 ratio of base perimeters ratio of heights 1: 3 ratio of lateral areas 4 : 49 ratio of total areas ratio of volumes 125: 216 27 :1000 9. Two similar cones have volumes of 27 and 64. Find the ratio of: a. the radii b. the slant height c. the lateral areas 10. Two spheres have radii 5 cm and 7 cm. Find the ratio of: a. the areas b. the volumes 11. Two foam plastic balls have scale factor 2 : 3. a. If the smaller ball has radius 6 cm, what is the radius of the larger ball? b. If the area of the larger ball is 36 cm 2, what is the area of the smaller ball? c. If the larger ball weighs 12 g, about how much does the smaller ball weigh? (Hint: Weight is related to volume.) 17
Geometry Review 11.3, 11.5, 11.7 Review: Surface Area & Volume of Pyramids, Cones & ~ Solids Find the surface area and volume of each figure. 3. 4. 5. Two cones have radii 8 and 12. The heights are 20 and 30. Are the cones similar? 6. The heights of two right prisms are 9 and 15. The bases are squares with sides 27 and 45. Are the prisms similar? Find the indicated ratios for the given solids. 7. Two similar cylinders with radii 5 and 8 a. heights b. total areas c. volumes 8. Two similar pyramids with heights 3 and 5 a. base areas b. total areas 9. Two balls made of the same material have radii 9 cm and 12 cm. If the smaller ball weighs 3 kg, find the weight of the larger ball to the nearest 0.1 kg. 18
Geometry Review Chapter 11 Review Find the surface area and volume of each figure. 3. 4. 12 yd 5. 6. 7. 8. (Find volume only.) 19
9. The circumference of a standard baseball is about 9 in. About how many square in. of horsehide are required to cover 100 balls, to the nearest whole number? 10. The volumes of two similar prisms are 891 cm 3 and 33 cm 3. The surface area of the larger prism is 153 cm 2. What is the surface area of the smaller prism? 11. What is the cross section formed in the figure at right? 12. A cylinder has a height of 5 mm and a volume of 80 mm 3. What is the radius of the base to the nearest tenth? Determine whether the two figures are similar. If so, give the scale factor of the first figure to the second figure. 13. 14. 20