Lesson 1-7
description
Transcript of Lesson 1-7
![Page 1: Lesson 1-7](https://reader036.fdocuments.us/reader036/viewer/2022062518/56814033550346895dab973c/html5/thumbnails/1.jpg)
Lesson 1-7
Three-Dimensional Figures
![Page 2: Lesson 1-7](https://reader036.fdocuments.us/reader036/viewer/2022062518/56814033550346895dab973c/html5/thumbnails/2.jpg)
Lesson 1-7
Lesson Outline
Five-Minute Check
Then & Now and Objectives
Vocabulary
Key Concept
Examples
Lesson Checkpoints
Summary and Homework
![Page 3: Lesson 1-7](https://reader036.fdocuments.us/reader036/viewer/2022062518/56814033550346895dab973c/html5/thumbnails/3.jpg)
Lesson 1-7
Then and Now
You measured and classified angles.
• Identify and use special pairs of angles
• Identify perpendicular lines
![Page 4: Lesson 1-7](https://reader036.fdocuments.us/reader036/viewer/2022062518/56814033550346895dab973c/html5/thumbnails/4.jpg)
Lesson 1-7
Objectives
• Identify and name three-dimensional figures
• Find surface area and volume
![Page 5: Lesson 1-7](https://reader036.fdocuments.us/reader036/viewer/2022062518/56814033550346895dab973c/html5/thumbnails/5.jpg)
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
![Page 6: Lesson 1-7](https://reader036.fdocuments.us/reader036/viewer/2022062518/56814033550346895dab973c/html5/thumbnails/6.jpg)
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
![Page 7: Lesson 1-7](https://reader036.fdocuments.us/reader036/viewer/2022062518/56814033550346895dab973c/html5/thumbnails/7.jpg)
Lesson 1-7
3-D Introduction
• Review of figures introduced in grade school Geometry
• Covered in detail in Chapter 12
• Formulas on formula sheet
![Page 8: Lesson 1-7](https://reader036.fdocuments.us/reader036/viewer/2022062518/56814033550346895dab973c/html5/thumbnails/8.jpg)
Lesson 1-7
Key Concept
• 3-d polygon
• Curved surface
![Page 9: Lesson 1-7](https://reader036.fdocuments.us/reader036/viewer/2022062518/56814033550346895dab973c/html5/thumbnails/9.jpg)
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
![Page 10: Lesson 1-7](https://reader036.fdocuments.us/reader036/viewer/2022062518/56814033550346895dab973c/html5/thumbnails/10.jpg)
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
![Page 11: Lesson 1-7](https://reader036.fdocuments.us/reader036/viewer/2022062518/56814033550346895dab973c/html5/thumbnails/11.jpg)
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
![Page 12: Lesson 1-7](https://reader036.fdocuments.us/reader036/viewer/2022062518/56814033550346895dab973c/html5/thumbnails/12.jpg)
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
![Page 13: Lesson 1-7](https://reader036.fdocuments.us/reader036/viewer/2022062518/56814033550346895dab973c/html5/thumbnails/13.jpg)
Lesson 1-7
Key Concept
• Formulas on formula sheet for all of these
![Page 14: Lesson 1-7](https://reader036.fdocuments.us/reader036/viewer/2022062518/56814033550346895dab973c/html5/thumbnails/14.jpg)
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
![Page 15: Lesson 1-7](https://reader036.fdocuments.us/reader036/viewer/2022062518/56814033550346895dab973c/html5/thumbnails/15.jpg)
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
![Page 16: Lesson 1-7](https://reader036.fdocuments.us/reader036/viewer/2022062518/56814033550346895dab973c/html5/thumbnails/16.jpg)
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
![Page 17: Lesson 1-7](https://reader036.fdocuments.us/reader036/viewer/2022062518/56814033550346895dab973c/html5/thumbnails/17.jpg)
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
![Page 18: Lesson 1-7](https://reader036.fdocuments.us/reader036/viewer/2022062518/56814033550346895dab973c/html5/thumbnails/18.jpg)
Lesson 1-7
Lesson Checkpoints
![Page 19: Lesson 1-7](https://reader036.fdocuments.us/reader036/viewer/2022062518/56814033550346895dab973c/html5/thumbnails/19.jpg)
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