Space Figures & Cross- Sections Section 11-1. Vocab Polyhedron - 3-dimensional figure whose surfaces...
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Transcript of Space Figures & Cross- Sections Section 11-1. Vocab Polyhedron - 3-dimensional figure whose surfaces...
Space Figures & Cross-Sections
Section 11-1
Vocab• Polyhedron - 3-dimensional figure
whose surfaces are polygons• Face of polyhedron - each polygon
that forms the polyhedron• Edge - segment formed by the
intersection of two faces• Vertex - point where 3 or more
edges intersect • Cross-section – the intersection of
a solid & a plane.
Vocab Ctd.
Euler’s Formula
Group Activity
• Each group will construct several 3-dimensional figures from nets
• Groups will then record data and make conjectures on the relationship between faces, edges and vertices of a polyhedron
Use Euler’s Formula to find the number of edges on a solid with 6 faces and 8 vertices.
F + V = E + 2 Euler’s Formula
6 + 8 = E + 2 Substitute the number of faces and vertices.
12 = E Simplify.
A solid with 6 faces and 8 vertices has 12 edges.
You try
• Use Euler’s formula to find the number of edges on a polyhedron with eight triangular faces.
• 12 edges
Cross SectionsDescribe this cross section.
The plane is parallel to the triangular base of the figure, so the cross section is also a triangle.
You try
• Describe the cross-section.
Drawing Cross Sections
Draw and describe a cross section formed by a vertical plane intersecting the top and bottom faces of a cube.
If the vertical plane is parallel to opposite faces, the cross section is a square.
Sample: If the vertical plane is not parallel to opposite faces, the cross section is a rectangle.
You try
• Draw & describe the cross section formed by a horizontal plane intersecting the left and right faces of the cube.
Closure