1. CCSS 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.

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

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

4. A solid with all flat surfaces that enclose a single region of space is called a polyhedron. Each flat surface is called a face. The line segments where the faces intersect are called edges. The point where 3 or more edges meet is called the vertex. Polyhedrons are named by the shape of their bases.

5. Concept

6. Example 1 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.

7. 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

8. Example 1 Identify Solids B. Determine whether the solid is a polyhedron. Then identify the solid.

9. Example 1 Identify Solids The solid is formed by polygonal faces, so it is a polyhedron. The bases are hexagons. This solid is a hexagonal prism.

10. 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.

11. 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

12. Example 1 A. Identify the solid.

13. Example 1 B. Identify the solid.

14. Example 1 C. Identify the solid.

15. Do p. 70 – 71 1, 6, 9, 12, 15 as a class

16. A polyhedron is a regular polyhedron if all of its faces are regular congruent polygons and all the edges are congruent. There are exactly 5 types of regular polyhedrons. See p. 68. They are called Platonic Solids since Plato used them a lot.

17. Concept

18. Surface Area is a 2-dimensional measurement of the surface of a solid figure. The surface area is the sum of the areas of each faces. Volume is the measurement of the amount of space enclosed by a solid figure.

19. Concept

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

21. Example 2 Find Surface Area and Volume Answer: The cone has a surface area of about 75.4 cm 2 and a volume of about 37.7 cm 3. r = 3, h = 4 Volume of a cone Simplify. Use a calculator.

22. Example 2 Find the surface area and volume of the triangular prism.

23. Example 3 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 and volume of the box.