Download presentation

Presentation is loading. Please wait.

Published byVincent McDonald Modified over 6 years ago

1
Surface Area and Volume Chapter 12

2
Exploring Solids 12.1 California State Standards 8, 9: Solve problems involving the surface area and lateral area of geometric solids and COMMIT TO MEMORY THE NECESSARY FORMULAS.

3
definition Polyhedron A 3-dimensional solid figure formed by polygons. Faces: the polygons that form the polyhedron Edges: a line segment formed by the intersection of two faces. Vertex: the point where 3 or more edges meet. face edge vertex Plural: polyhedra

4
examples Polyhedra Prism Pyramid Non-Polyhedra Cylinder Cone Sphere

5
definition Regular Polyhedron All faces are congruent regular polygons

6
definition Convex Polyhedron A polyhedron where any line segment between any two points lies entirely within the polyhedron convex non-convex

7
definition Platonic Solids 5 regular, convex polyhedra Tetrahedron4 equilateral triangles Hexahedron6 squares Octahedron8 equilateral triangles Dodecahedron12 regular pentagons Icosahedron20 equilateral triangles

8
tetrahedron 4 faces octahedron 8 faces hexahedron 6 faces (cube) dodecahedron 12 faces icosahedron 20 faces

9
definition Cross-section The intersection of a plane and a solid.

10
definition Cross-section The intersection of a plane and a solid.

11
theorem Euler’s Theorem The number of faces (F), vertices (V), and edges (E) of a polyhedron are related by the formula F + V – E = 2

12
example A solid has 10 faces. 4 triangles 1 square 4 hexagons1 octagon. How many vertices does the solid have?

13
example 4 triangles have 4(3) = 12 sides 1 square has 4 sides 4 hexagon has 4(6) = 24 sides 1 octagon has 8 sides 48 individual sides Each side is shared by two polygons edges in the polyhedron

14
example F + V – E = 2 10 + V – 24 = 2 -14 + V = 2 V = 16

15
example A soccer ball is made of 12 pentagons and 20 hexagons. How many vertices does the soccer ball have? 12 pentagons have 12(5) = 60 sides 20 hexagons have 20(6) = 120 sides 180 individual sides Each side is shared by two polygons edges in the polyhedron

16
example F + V – E = 2 32 + V – 90 = 2 -58 + V = 2 V = 60

Similar presentations

© 2021 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google