Math 8: Identify Shapes and Surface Area

Transcription

1 Name: Class: Date: Math 8: Identify Shapes and Surface Area 1. Name the solid according to its description: The figure has one base that is a rectangle and four lateral surfaces that are triangles. 2. Name the solid according to its description: The figure has one base that is a circle. 3. Name the solid according to its description: The figure has one base that is a square and four lateral surfaces that are triangles. 4. Name the solid according to its description: The figure has two bases that are parallel congruent trapezoids. 5. Name the solid according to its description: The figure has one base that is a hexagon. 6. Name the solid according to its description: The figure has two bases that are parallel congruent circles. 7. Name the solid according to its description: The figure has two bases that are congruent and parallel hexagons. 8. Name the solid according to its description: The figure has five lateral surfaces that are triangles. 9. A solid with two parallel and congruent bases cannot be which of the following? a. cone b. prism c. cylinder d. cube Use a formula to find the surface area of the figure

2 Name: When Tyson opens a cereal box and lays it out flat, he sees that both the top and the bottom of the box measure 3 inches by 9 inches. Both sides of the box measure 3 inches by 12 inches, and both the front and back of the box measure 9 inches by 12 inches. What is the surface area of the cereal box? 14. a sphere with a radius of 5 cm 15. 2

3 Name: Determine which of these cylinders has the largest surface area. a. a cylinder with a height of 4 cm and a base with a radius of 8 cm b. a cylinder with a height of 8 cm and a base with a radius of 4 cm c. a cylinder with a height of 6 cm and a base with a radius of 3 cm d. a cylinder with a height of 8 cm and a base with a radius of 3 cm Find the surface area of the figure. Round your answer to the nearest hundredth, if necessary

4 Name: 20. The tent below is a square pyramid with a base edge length of 8 feet and a slant height of 6 feet. There is a doorway that zips into the opening to keep mosquitoes out. Find the lateral area of the tent to determine how many square feet of material was needed to create the sides of the tent. 21. Use a formula to find the surface area of the square pyramid. Find the surface area of the solid. Round to the nearest whole unit, if necessary. 22. a square pyramid with a base edge length of 15 m and a slant height of 36 m 23. a square pyramid with a base area of 9 ft 2 and a slant height of 8 ft 4

5 Name: A square pyramid has a 10-cm base and slant height of 15 cm. A cone has a base diameter of 10 cm and a slant height of 15 cm. Which has a greater surface area? Explain. 27. Describe the similarities and differences between a triangular prism and a triangular pyramid. 5

6 Math 8: Identify Shapes and Surface Area Answer Section 1. ANS: rectangular pyramid 2. ANS: cone 3. ANS: square pyramid 4. ANS: trapezoidal prism 5. ANS: hexagonal pyramid 6. ANS: cylinder 1

7 7. ANS: hexagonal prism 8. ANS: pentagonal pyramid 9. ANS: A PTS: 1 DIF: L3 REF: 8-1 Solids OBJ: Naming Solids KEY: naming solids cone 10. ANS: 574 in. 2 PTS: 1 DIF: L2 REF: 8-4 Surface Areas of Prisms and Cylinders TOP: 8-4 Example 2 KEY: surface area prism 11. ANS: 2,700 yd 2 PTS: 1 DIF: L2 REF: 8-4 Surface Areas of Prisms and Cylinders TOP: 8-4 Example 2 KEY: surface area prism 12. ANS: 2,280 cm 2 PTS: 1 DIF: L2 REF: 8-4 Surface Areas of Prisms and Cylinders TOP: 8-4 Example 2 KEY: surface area prism 2

8 13. ANS: 342 in. 2 PTS: 1 DIF: L3 REF: 8-4 Surface Areas of Prisms and Cylinders TOP: 8-4 Example 1 KEY: surface area prism word problem 14. ANS: 314 cm 2 PTS: 1 DIF: L2 REF: 8-8 Spheres OBJ: Surface Area and Volume of a Sphere STA: 8MI A.PA MI G.SR MI G.SR TOP: 8-8 Example ANS: 432 yd 2 PTS: 1 DIF: L2 REF: 8-4 Surface Areas of Prisms and Cylinders TOP: 8-4 Example 2 KEY: surface area prism 16. ANS: 4,590 cm 2 PTS: 1 DIF: L2 REF: 8-4 Surface Areas of Prisms and Cylinders TOP: 8-4 Example 2 KEY: surface area prism 17. ANS: A PTS: 1 DIF: L3 REF: 8-4 Surface Areas of Prisms and Cylinders OBJ: Finding Surface Areas of Cylinders TOP: 8-4 Example 3 KEY: surface area cylinder 18. ANS: in. 2 ; in. 2 PTS: 1 DIF: L3 REF: 8-4 Surface Areas of Prisms and Cylinders OBJ: Finding Surface Areas of Cylinders TOP: 8-4 Example 3 KEY: surface area lateral area cylinder 3

9 19. ANS: cm 2 ; cm 2 PTS: 1 DIF: L3 REF: 8-4 Surface Areas of Prisms and Cylinders OBJ: Finding Surface Areas of Cylinders TOP: 8-4 Example 3 KEY: surface area lateral area cylinder 20. ANS: 96 ft 2 PTS: 1 DIF: L2 REF: 8-5 Surface Areas of Pyramids and Cones OBJ: Finding Surface Areas of Pyramids TOP: 8-5 Example 2 KEY: surface area pyramid slant height word problem 21. ANS: 45 ft 2 PTS: 1 DIF: L2 REF: 8-5 Surface Areas of Pyramids and Cones OBJ: Finding Surface Areas of Pyramids TOP: 8-5 Example 3 KEY: surface area pyramid 22. ANS: 1,305 m 2 PTS: 1 DIF: L3 REF: 8-5 Surface Areas of Pyramids and Cones OBJ: Finding Surface Areas of Pyramids TOP: 8-5 Example 3 KEY: surface area pyramid slant height 23. ANS: 57 ft 2 PTS: 1 DIF: L4 REF: 8-5 Surface Areas of Pyramids and Cones OBJ: Finding Surface Areas of Pyramids TOP: 8-5 Example 3 KEY: surface area pyramid slant height 4

10 24. ANS: 138 in. 2 PTS: 1 DIF: L3 REF: 8-5 Surface Areas of Pyramids and Cones OBJ: Finding Surface Areas of Cones TOP: 8-5 Example 4 KEY: surface area cone 25. ANS: 792 yd 2 PTS: 1 DIF: L2 REF: 8-5 Surface Areas of Pyramids and Cones OBJ: Finding Surface Areas of Cones TOP: 8-5 Example 4 KEY: surface area cone 26. ANS: The square pyramid; S.A. = L.A. + B, so the surface area of the pyramid is 2(10)(15) , or 400 cm 2. Ê The surface area of the cone is π( 5) ( 15) + π 5 2 ˆ ËÁ, or 100π 314 cm 2. PTS: 1 DIF: L3 REF: 8-5 Surface Areas of Pyramids and Cones OBJ: Finding Surface Areas of Cones TOP: 8-5 Example 4 KEY: surface area pyramid cone slant height 27. ANS: Answers may vary. Sample: Both solids have triangular bases. A triangular prism as two bases, while a triangular pyramid has only one. Both solids have three lateral faces. The lateral faces of a triangular prism are rectangles, while the lateral faces of a triangular pyramid are triangles. Unlike a triangular prism, a triangular pyramid has a vertex. KEY: prism pyramid writing in math DOK: DOK 3 5