Lesson 1-7

Three-Dimensional Figures

Lesson 1-7

Lesson Outline

Five-Minute Check

Then & Now and Objectives

Vocabulary

Key Concept

Examples

Lesson Checkpoints

Summary and Homework

Lesson 1-7

Then and Now

You measured and classified angles.

• Identify and use special pairs of angles

• Identify perpendicular lines

Lesson 1-7

Objectives

• Identify and name three-dimensional figures

• Find surface area and volume

Lesson 1-7

Vocabulary• Polyhedron – a solid with all flat surfaces that enclose a single

region of space

• Face – a flat surface of a polyhedron

• Edge – line segments where faces intersect

• Vertex – a point where three or more edges intersect

• Base – parallel faces in a prism

• Surface area – two-dimensional measurement of the surface of a solid figure

• Volume – the measure of the amount of space enclosed by a solid figure

Lesson 1-7

Vocabulary• Platonic solid – the five types of regular polyhedrons

• Prism – a solid with two parallel congruent faces connected by parallelogram faces

• Cylinder – a solid with congruent parallel circular bases connected by a curved surface

• Cone – a solid with a circular base connected by a curved surface to a single vertex

• Pyramid – a polyhedron that has a polygonal base and three or more triangular faces that meet at a common vertex

• Sphere – a set of points in space that are the same distance from a given point

• Regular polyhedron – all of its faces are regular congruent polygons and all edges are congruent

Lesson 1-7

3-D Introduction

• Review of figures introduced in grade school Geometry

• Covered in detail in Chapter 12

• Formulas on formula sheet

Lesson 1-7

Key Concept

• 3-d polygon

• Curved surface

Lesson 1-7

Example 1ADetermine whether the solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices.

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,

ABDCFaces: rectangles FBDH, EACG, GCDH,

EFBA, EFHG, ABDC

Vertices: A, B, C, D, E, F, G, H

Lesson 1-7

Example 1B

The solid is formed by polygonal faces, so it is a polyhedron. The bases are hexagons. This solid is a hexagonal prism.

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

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

Lesson 1-7

Example 1CC. Determine whether the solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices.

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 TVertex: Wno faces or edges

Lesson 1-7

Key Concept

• Most of these are not seen in HS Geometry– cube is seen alot

• Formulas on formula sheet for ones we need

Lesson 1-7

Key Concept

• Formulas on formula sheet for all of these

Lesson 1-7

Example 2Find the surface area and volume of the cone.

Surface area of a coneSA = rl + r²

r = 3, l = 5SA = (3)(5) + (3)²

SimplifySA = 24

Use a calculator.SA 75.4 cm²

Lesson 1-7

Example 2 contFind the surface area and volume of the cone.

Answer: The cone has a surface area of about 75.4 cm2 and a volume of about 37.7 cm3.

Volume of a cone

r = 3, h = 4

Simplify.V = 12

Use a calculator.V 37.7 cm³

Lesson 1-7

Example 3AA. CONTAINERS Mike is creating a mailing tubewhich can be used to mail posters and architectural plans. The diameter of the base is 3.75 inches, and the height is 2.67 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.

Answer: Mike needs about 399.1 square inches ofcardboard to make the tube.

Surface area of a cylinderSA = 2rh + 2r²

r = 1.875 in., h = 32 in.SA = 2(1.875)(32) + 2(1.875)²

Use a calculator.SA 399.1 in²

Lesson 1-7

Example 3B

B. CONTAINERS Mike is creating a mailing tubewhich can be used to mail posters and architectural plans. The diameter of the base is 3.75 inches, and the height is 2.67 feet. Find the volume of the tube.

V = π(1.875)²(32) r = 1.875 in., h = 32 in.

Use a calculator.V ≈ 353.4

Answer: The volume of the tube is about 353.4 cubic inches.

V = πr²h

Lesson 1-7

Lesson Checkpoints

Lesson 1-7

Summary & Homework

• Summary:– Most three-dimensional figures have bases, faces,

edges, and vertices (corners)– Many three-dimensional figures are named for their

bases– The surface area of a three-dimensional figures can

be determined by formulas on the formula sheet– The volume of a three-dimensional figures can be

determined by formulas on the formula sheet

• Homework: – pg 70-3: 18-23