1. Three-Dimensional Figures
LESSON 1–7
Three-Dimensional Figures

2. Five-Minute Check (over Lesson 1–6) TEKS Then/Now New Vocabulary
Key Concept: Types of Solids
Example 1: Identify Solids
Key Concept: Platonic Solids
Key Concept: Surface Area and Volume
Example 2: Find Surface Area and Volume
Example 3: Real-World Example: Surface Area and Volume
Lesson Menu

3. Name polygon A by its number of sides.
A. pentagon
B. heptagon
C. octagon
D. decagon
5-Minute Check 1

4. Name polygon B by its number of sides.
A. pentagon
B. hexagon
C. heptagon
D. octagon
5-Minute Check 2

5. Find the perimeter of polygon A.
A. 25 cm
B. 35 cm
C. 40 cm
D. 45 cm
5-Minute Check 3

6. Find the perimeter of polygon B.
A. 40 in.
B. 42 in.
C. 45 in.
D. 85 in.
5-Minute Check 4

7. Classify the polygons as regular or irregular.
A. polygon A: regular polygon B: regular
B. polygon A: regular polygon B: irregular
C. polygon A: irregular polygon B: regular
D. polygon A: irregular polygon B: irregular
5-Minute Check 5

8. A regular hexagon has a perimeter of 90 meters
A regular hexagon has a perimeter of 90 meters. What is the length of one side of the hexagon?
A. 18 meters
B. 10 meters
C meters
D. 15 meters
5-Minute Check 6

9. Mathematical Processes G.1(A), Also addresses G.1(F)
Targeted TEKS
G.11(C) Apply the formulas for the total and lateral
surface area of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to
solve problems using appropriate units of measure.
G.11(D) Apply the formulas for the volume of three-dimensional
figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure. Also addresses G.10(B).
Mathematical Processes
G.1(A), Also addresses G.1(F)
TEKS

10. You identified and named two-dimensional figures.
Identify and name three-dimensional figures.
Find surface area and volume.
Then/Now

11. polyhedron cylinder cone sphere face edge regular polyhedron vertex
Platonic solid
surface area
volume
face
edge
vertex
prism
base
pyramid
Vocabulary

12. Concept

13. Identify Solids
A. Determine whether the solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices.
Example 1

14. Identify Solids
The solid is formed by polygonal faces, so it is a polyhedron. The bases are rectangles. This solid is a rectangular prism.
Answer: rectangular prism; Bases: rectangles EFHG, ABDC Faces: rectangles FBDH, EACG, GCDH, EFBA, EFHG, ABDC
Vertices: A, B, C, D, E, F, G, H
Example 1

15. Identify Solids
B. Determine whether the solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices.
Example 1

16. Answer: hexagonal prism; Bases: hexagon EFGHIJ and hexagon KLMNOP
Identify Solids
The solid is formed by polygonal faces, so it is a polyhedron. The bases are hexagons. This solid is a hexagonal prism.
Answer: hexagonal prism; Bases: hexagon EFGHIJ and hexagon KLMNOP
Faces: rectangles EFLK, FGML, GHNM, HNOI, IOPJ, JPKE; hexagons EFGHIJ and KLMNOP
Vertices: E, F, G, H, I, J, K, L, M, N, O, P
Example 1

17. Identify Solids
C. Determine whether the solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices.
Example 1

18. Answer: Base: circle T Vertex: W no faces or edges
Identify Solids
The solid has a curved surface, so it is not a polyhedron. The base is a circle and there is one vertex. So, it is a cone.
Answer: Base: circle T Vertex: W no faces or edges
Example 1

19. A. Identify the solid. A. triangular pyramid B. pentagonal prism
C. rectangular prism
D. square pyramid
Example 1

20. B. Identify the solid. A. cone B. cylinder C. pyramid D. polyhedron
Example 1

21. C. Identify the solid. A. triangular prism B. triangular pyramid
C. rectangular pyramid
D. cone
Example 1

22. Concept

23. Concept

24. Find the surface area and volume of the cone.
Find Surface Area and Volume
Find the surface area and volume of the cone. π .
Use a calculator.
Example 2

25. Volume of a cone r = 3, h = 4 Simplify. Use a calculator.
Find Surface Area and Volume
Volume of a cone
r = 3, h = 4
Simplify.
Use a calculator.
Answer: The cone has a surface area of about cm2 and a volume of about 37.7 cm3.
Example 2

26. Find the surface area and volume of the triangular prism.
A. surface area = 288 ft2 volume = 336 ft3
B. surface area = 336 ft2 volume = 288 ft3
C. surface area = 26 ft2 volume = 60 ft3
D. surface area = 488 ft2 volume = 122 ft3
Example 2

27. Surface Area and Volume
A. CONTAINERS Mike is creating a mailing tube which can be used to mail posters and architectural plans. The diameter of the base is inches, and the height is feet. Find the amount of cardboard Mike needs to make the tube.
The amount of material used to make the tube would be equivalent to the surface area of the cylinder.
Example 3

28. Surface area of a cylinder
Surface Area and Volume
Surface area of a cylinder
r = in., h = 32 in.
Use a calculator.
399.1
Answer: Mike needs about square inches of cardboard to make the tube.
Example 3

29. Surface Area and Volume
B. CONTAINERS Mike is creating a mailing tube which can be used to mail posters and architectural plans. The diameter of the base is inches, and the height is feet. Find the volume of the tube.
Volume of a cylinder
r = in., h = 32 in.
Use a calculator.
353.4
Example 3

30. Answer: The volume of the tube is about 353.4 cubic inches.
Surface Area and Volume
Answer: The volume of the tube is about cubic inches.
Example 3

31. A. Jenny has some boxes for shipping merchandise
A. Jenny has some boxes for shipping merchandise. Each box is in the shape of a rectangular prism with a length of 18 inches, a width of 14 inches, and a height of 10 inches. Find the surface area of the box.
A. surface area = 2520 in2
B. surface area = 18 in2
C. surface area = 180 in2
D. surface area = 1144 in2
Example 3

32. B. Jenny has some boxes for shipping merchandise
B. Jenny has some boxes for shipping merchandise. Each box is in the shape of a rectangular prism with a length of 18 inches, a width of 14 inches, and a height of 10 inches. Find the volume of the box.
A. volume = 1144 in3
B. volume = 14 in3
C. volume = 2520 in3
D. volume = 3600 in3
Example 3

33. Three-Dimensional Figures
LESSON 1–7
Three-Dimensional Figures