11-1 Exploring 3D figures I. Polyhedra – solids with all flat surfaces that are not open

SPHERE CYLINDER CONE PYRAMID CUBE PRISM

II. Prisms A polyhedron with two congruent faces that are polygons contained in parallel lines

Parts of a prism FACE Faces — The flat surfaces of a solid object.

EDGE Edges — the line segments where the faces intersect

BASE The two congruent faces of a prism

LATERAL FACE The other faces of the prism which connect the two bases.

LATERAL EDGES

Platonic Solids

III. Regular Polyhedra All of its faces are shaped like congruent regular polygons

IV. Slices

V. Examples 1. Draw a top, left, front, and right view of this model.

2. Identify the solid. Name its bases, faces, edges, and vertices.

3. Identify the polyhedra. Name its bases, faces, edges, and vertices.

4. Miranda has a piece of foam that is shaped like a cone. She wants to make a decorative centerpiece for a table using the cone. However, she does not want the centerpiece to have a point, but wants the top of the centerpiece to be an oval shape. How should she cut the cone to get an oval top?

11-3 Surface Area Prism and Cylinder I. Prisms Oblique: Tilted at an angle; neither vertical nor horizontal Right: altitude is the height

II. Types of right prisms RECTANGULAR HEXAGONAL TRIANGULAR

III. RIGHT PRISM PARTS

IV. VARIABLES USED FOR PRISMS B- BASE L- LATERAL AREA P- PERIMETER OF BASE H- HEIGHT OF PRISM

Lateral Area of a Right Prism LA = P * H V. FORMULAS

Surface Area of Right prism SA = P * H + 2 B

Examples: 1. Find the L and SA of a right triangular prism with a height of 10 inches and a right triangular base with legs of 10 and 12 inches.

VI. Cylinders 2 BASES ARE CIRCLES

HEIGHT

RADIUS

LA = 2  R H

Surface area of a cylinder

Example 2. Find the Lateral Area and the Surface Area.

11-4 Surface area Pyramids and Cones

BASE

FACE

HEIGHT

EDGES

SLANT HEIGHT

S A = ½ * P * L + B

CONE BASE IS A CIRCLE

HEIGHT

RADIUS

SLANT HEIGHT