Five-Minute Check (over Lesson 1–7) Mathematical Practices 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

Identify the type of rigid transformation shown as a reflection, translation, or rotation. B. translation C. rotation 5-Minute Check 1

Identify the type of rigid transformation shown as a reflection, translation, or rotation. B. translation C. rotation 5-Minute Check 2

Triangle LMN has vertices L(–4, 5), M(–4, 1), N(0, 3) Triangle LMN has vertices L(–4, 5), M(–4, 1), N(0, 3). Triangle PQR has vertices P(1, –1),Q(1, –5), and R(5, –3). Identify the transformation. A. reflection B. translation C. rotation 5-Minute Check 3

Rectangle RSTU has vertices at (0, 0), (0, 4), (6, 4), and (6, 0) Rectangle RSTU has vertices at (0, 0), (0, 4), (6, 4), and (6, 0). Which of the following is a vertex of the rectangle reflected over the x-axis? A. (–6, 0) B. (–4, –6) C. (0, –4) D. (–4, 0) 5-Minute Check 4

Mathematical Practices 2 Reason abstractly and quantitatively. 6 Attend to precision. Content Standards G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. G.MG.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). MP

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

Concept

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

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 so it is not a polyhedron 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

Concept

Concept

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