Space Figures and Cross Sections
11-1
Space Figures and
Cross Sections
Polyhedron:
a space figure, or
three-dimensional figure,
whose surfaces are polygons
Face:
the flat surface of a
figure
Edge:
Formed by the
intersection of two faces
Vertex:
the point where three
or more edges intersect
Problem 1: Identifying Vertices, Edges,
and Faces
How many vertices, edges, and faces are in
the polyhedron? List them.
Euler’s Formula
Problem 2: Using Euler’s Formula
For each polyhedron, use Euler’s Formula
to find the missing number
For each polyhedron, use Euler’s Formula
to find the missing number
Problem 4: Describing a Cross Section
Cross Section:
the intersection of a solid and a plane
(a thin slice of the solid)
What is the cross section formed by the plane and
the solid below?
What is the cross section formed by a horizontal
plane?
What is the cross section formed by a vertical plane?
Problem 5: Drawing a Cross Section
Draw a cross section formed by a vertical plane
intersecting the front face and right face of the
cube. What shape is the cross section?
Draw a cross section formed by a horizontal
plane intersecting left and right faces of the
cube. What shape is the cross section?
Delve into the world of polyhedrons, vertices, edges, and faces. Explore Euler's Formula to uncover missing numbers within various polyhedrons. Learn about cross sections formed by planes intersecting solid figures, and discover the shapes created in the process.
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Presentation Transcript
11-1 Space Figures and Cross Sections
Polyhedron: a space figure, or three-dimensional figure, whose surfaces are polygons Vertex Edge Face: the flat surface of a figure Edge: Formed by the intersection of two faces Faces Vertex: the point where three or more edges intersect
Problem 1: Identifying Vertices, Edges, and Faces How many vertices, edges, and faces are in the polyhedron? List them.
Eulers Formula ? + ? = ? + 2 F = faces V = vertices E = Edges
Problem 2: Using Eulers Formula For each polyhedron, use Euler s Formula to find the missing number
For each polyhedron, use Eulers Formula to find the missing number
Problem 4: Describing a Cross Section Cross Section: the intersection of a solid and a plane (a thin slice of the solid) What is the cross section formed by the plane and the solid below?
What is the cross section formed by a horizontal plane? What is the cross section formed by a vertical plane?
Problem 5: Drawing a Cross Section Draw a cross section formed by a vertical plane intersecting the front face and right face of the cube. What shape is the cross section?
Draw a cross section formed by a horizontal plane intersecting left and right faces of the cube. What shape is the cross section?
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