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Five-Minute Check (over Lesson 1–6) CCSS 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
Name polygon A by its number of sides. A. pentagon B. heptagon C. octagon D. decagon 5-Minute Check 1
Name polygon B by its number of sides. A. pentagon B. hexagon C. heptagon D. octagon 5-Minute Check 2
Find the perimeter of polygon A. A. 25 cm B. 35 cm C. 40 cm D. 45 cm 5-Minute Check 3
Find the perimeter of polygon B. A. 40 in. B. 42 in. C. 45 in. D. 85 in. 5-Minute Check 4
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
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. 11.25 meters D. 15 meters 5-Minute Check 6
Mathematical Practices 2 Reason abstractly and quantitatively. Content Standards G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. Mathematical Practices 2 Reason abstractly and quantitatively. 6 Attend to precision. CCSS
You identified and named two-dimensional figures. Identify and name three-dimensional figures. Find surface area and volume. Then/Now
polyhedron cylinder cone sphere face edge regular polyhedron vertex Platonic solid surface area volume face edge vertex prism base pyramid Vocabulary
Types of Solids The surfaces of a three-dimensional figure determines the type of solid it is. A polyhedron is a three-dimensional figure whose surfaces, or faces, are all polygons. Prisms and pyramids are two types of polyhedrons.
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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
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
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
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
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
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
A. Identify the solid. A. triangular pyramid B. pentagonal prism C. rectangular prism D. square pyramid Example 1
B. Identify the solid. A. cone B. cylinder C. pyramid D. polyhedron Example 1
C. Identify the solid. A. triangular prism B. triangular pyramid C. rectangular pyramid D. cone Example 1
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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
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 75.4 cm2 and a volume of about 37.7 cm3. Example 2
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
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
Surface area of a cylinder Surface Area and Volume Surface area of a cylinder r = 1.875 in., h = 32 in. Use a calculator. 399.1 Answer: Mike needs about 399.1 square inches of cardboard to make the tube. Example 3
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 = 1.875 in., h = 32 in. Use a calculator. 353.4 Example 3
Answer: The volume of the tube is about 353.4 cubic inches. Surface Area and Volume Answer: The volume of the tube is about 353.4 cubic inches. Example 3
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
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
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