Lesson 10 ~ Three-Dimensional Figures
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1 Lesson 10 ~ Three-Dimensional Figures Name a solid that fits each description. 1. a can of beans 2. a shoe box 3. a pyramid with five lateral faces 4. a solid with six vertices 5. a prism with bases shaped like hexagons 6. the moon 7. a pyramid with a base shaped like a trapezoid Tell whether each statement is true or false. If false, explain why. 8. A cone has one base. 9. All prisms have two bases. 10. A cone has two vertices. 11. The lateral faces of a pyramid are triangles. 12. A cylinder has one base. 13. A prism is named by the shape of its bases. Identify the number of lateral faces, bases, edges and vertices Describe the difference between a lateral face and a base.
2 Lesson 11 ~ Drawing Solids Sketch a net of each solid Cube Sketch a diagram of each solid. 5. Cone 6. Square prism 7. Pentagonal pyramid 8. Cylinder 9. Identify four real-world objects that would represent four different solids.
3 Lesson 12 ~ Surface Area of Prisms Find the surface area of each prism. 5 mm mm 6 ft 12 mm 4 ft 3 ft 2 m 9 m 2 m 1.7 m 2 m units 14.8 ft 13 in 5 in Base area = 32 u² Perimeter of base = 16 units Base area = 92.5 ft² Each side of the base is 6.8 ft 12 in in 7. Ramon has a storage box that is a hexagonal prism. The box has a lateral area of 342 cm². The bottom of the box is 68 cm². What is the total surface area of the storage box? 8. A triangular prism has a surface area 257 in². The lateral area is 201 in². Find the area of one of the bases. 9. An octagonal prism has a base area of 235 in². The surface area of the prism is 500 in². What is the lateral area of the prism? 10. A shoe box is 24 inches long, 12 inches wide and 8 inches deep. a. Find the area of one base of the box. b. What is the lateral area of the box? c. Calculate the surface area of the box. d. Use the formula 2(lw +wh + lh) from the Oregon State Assessment formula sheet to calculate the surface area of the box. Does it confirm your answer to part c? 11. One of the faces of a cube is 25 cm². What is its surface area of the cube?
4 Lesson 13 ~ Surface Area of Cylinders 1. The circumference of a cylindrical paint bucket is 18 inches. The paint bucket is 12 inches tall. Find the lateral area of the bucket. 2. The radius of a cylindrical soup can is 12 cm. Find the area of the paper label if the can is 10 cm tall. Use 3.14 for π. 3. The lateral area of a cylinder is 24 m². The area of one base is 9 m². What is the surface area of the cylinder? Find the surface area of each cylinder. Use 3.14 for π ft 34 m 5.5 in 8 ft 9 m in 7. A cylindrical storage container has a radius of 3 inches. It is 2.5 inches tall. a. Find the surface area of the storage container with a lid. b. Find the surface area of the storage container without a lid. 8. The circumference of a cylinder is 157 meters. The height of the cylinder is 12 meters. Use 3.14 for π. a. Find the lateral area. b. Find the length of the radius. c. What is the area of one base? d. Determine the total surface area.
5 Lesson 14 ~ Surface Area of Regular Pyramids Give a name of a pyramid with the given number of lateral faces. 1. five lateral faces 2. eight lateral faces 3. three lateral faces 4. Use the pyramid at the right. a. Draw a net of the pyramid. 7 cm b. Find the area of each figure of the net. 4 cm 4 cm c. Find the surface area of the pyramid. Find the lateral area of each pyramid Slant height = 9.4 in 2.5 cm 2.5 cm 6 cm 7 in 7 in 2.5 cm 2.5 cm 2.5 cm 7 in Find the surface area of each pyramid ft Each side of the base is 7.3 m. Area of the base = 138 m² Slant height = 14 m 12 ft 12 ft 9. Jaime is wrapping a ring. He put the ring in a square pyramidal box before wrapping it. The perimeter of the base of the box is 8 inches. The slant height of the box is 2.75 inches. How much wrapping paper will he need to cover the box exactly?
6 Lesson 15 ~ Surface Area of Cones Find the lateral area of each cone. Use 3.14 for π in cm 13 in 18.8 cm 3. The lateral area of a cone is ft². The slant height of the cone is 12 feet. Find the length of the radius. Find the surface area of each cone. Use 3.14 for π ft 6.5 mm 3.0 mm 72 m 48 m 6 ft 7. Barbara works at a plastics manufacturing company. She needs to calculate the surface area of a plastic cone. Barbara knows the diameter of each cone is 2 feet and the slant height is 4.5 feet. Find the surface area of the plastic cone. 8. Complete the table. Use different values of π to find the surface area of each cone. Surface Area Using Radius Slant height 22 Calculator π π, exact answer 7 14 meters 10 meters a. b. c. 3.5 mm 7 mm d. e. f.
7 Lesson 16 ~ Surface Area of Composite Solids Find the surface area of each composite solid. When necessary, use 3.14 for π in 11 m 5 m 2 in 2 in 17 m 2 in 3. 5 ft 4. 5 ft 6 cm 13 ft 9 cm 7 cm 10 ft 16 ft 12 cm 4 cm 2 cm 8 ft 10 cm 5. Sylvia makes ornaments to give to her friends as gifts. Each ornament is shaped like a square prism with a pyramid on top. She paints each ornament then adds a unique design. a. Sketch a diagram of an ornament. b. How many faces on the prism are on the outside surface? c. How many faces on the pyramid are on the outside surface? 6. Roger is putting up a greenhouse for his prize flowers. He has decided on a semicircular greenhouse, shown to the right. Calculate the amount of plastic needed to cover the greenhouse. 10 ft 15 ft
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