1.7 Three-Dimensional Figures Objective:Identify and name three-dimensional figures and find surface area and volume of the figures Describe the polyhedron or solid that can be made from a given net including the Platonic Solids. Extend the study of planar figures to three-dimensions, including the classical solid figures, and develop analysis through cross-sections. Give precise mathematical descriptions or definitions of geometric shapes in the plane and space. , Describe solids and/or surfaces in three-dimensional space when given two-dimensional representations for the surfaces of three-dimensional objects. , Develop and use special formulas relating to polyhedra (e.g., Euler’s Formula).

Polyhedron Solid with all flat surfaces Named by the Shape of Base Prism Pyramid Not Polyhedrons Cylinder Cone Sphere Named by the Shape of Base

Polyhedron

Is the solid is a polyhedron. Then identify the solid Is the solid is a polyhedron? Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices. rectangular prism; Bases: rectangles EFHG, ABDC Faces: rectangles FBDH, EACG, GCDH, EFBA, EFHG, ABDC Vertices: A, B, C, D, E, F, G, H

Determine whether the solid is a polyhedron. Then identify the solid Determine whether the solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices 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

Determine whether the solid is a polyhedron. Then identify the solid Determine whether the solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices Not a polyhedron

Regular Polyhedron All sides are regular congruent polygons

Surface Area and Volume Slant Height Height

Example Mike is creating a mailing tube which can be used to mail posters and architectural plans. The diameter of the base is 3 ¾ inches, and the height is 2 2/3 feet. Find the amount of cardboard Mike needs to make the tube. Surface area of a cylinder r = 1.875 in., h = 32 in. A = 399.1 Answer: Mike needs about 399.1 square inches of cardboard to make the tube.

Assignment Block Class Page 71, 6 - 26 even Extra Credit 1-7 Lab complete problems 1-12, 1 point each on Test

Assignment Honors Class Page 71, 12 - 28 every 4th, 32,34,38 Complete Lab 1.7 problems 2-12 even