Vocabulary A polyhedron is a three-dimensional solid with flat surfaces and straight edges. Each...
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Transcript of Vocabulary A polyhedron is a three-dimensional solid with flat surfaces and straight edges. Each...
![Page 1: Vocabulary A polyhedron is a three-dimensional solid with flat surfaces and straight edges. Each polygon is a face of the polyhedron. An edge is a segment.](https://reader036.fdocuments.net/reader036/viewer/2022062322/56649f505503460f94c7363a/html5/thumbnails/1.jpg)
Vocabulary
A polyhedron is a three-dimensional solid with flat surfaces and straight edges.
Each polygon is a face of the polyhedron.
An edge is a segment that is formed by the intersection of two faces.
A vertex is a point where three or more edges intersect.
A net is a two-dimensional pattern that you can fold to form a three-dimensional figure.
One of the simplest such figures is a cube — a polyhedron with six faces, each of which is a square.
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Vocabulary Prisms: polyhedron with 2 congruent and parallel faces
called bases.
Pyramid: polyhedron in which 1 face is a polygon and the others are triangles…comes to a point at the top.
Cylinder: 3D figure with 2 congruent & parallel bases that are circles
Cone: has 1 circular base and comes to a point at top
![Page 3: Vocabulary A polyhedron is a three-dimensional solid with flat surfaces and straight edges. Each polygon is a face of the polyhedron. An edge is a segment.](https://reader036.fdocuments.net/reader036/viewer/2022062322/56649f505503460f94c7363a/html5/thumbnails/3.jpg)
Vocabulary
Cross Section:
The intersection of a solid and a plane. The result is a polygon.
![Page 4: Vocabulary A polyhedron is a three-dimensional solid with flat surfaces and straight edges. Each polygon is a face of the polyhedron. An edge is a segment.](https://reader036.fdocuments.net/reader036/viewer/2022062322/56649f505503460f94c7363a/html5/thumbnails/4.jpg)
Identifying a Net
![Page 5: Vocabulary A polyhedron is a three-dimensional solid with flat surfaces and straight edges. Each polygon is a face of the polyhedron. An edge is a segment.](https://reader036.fdocuments.net/reader036/viewer/2022062322/56649f505503460f94c7363a/html5/thumbnails/5.jpg)
Identifying a Net
![Page 6: Vocabulary A polyhedron is a three-dimensional solid with flat surfaces and straight edges. Each polygon is a face of the polyhedron. An edge is a segment.](https://reader036.fdocuments.net/reader036/viewer/2022062322/56649f505503460f94c7363a/html5/thumbnails/6.jpg)
Identifying a Net
![Page 7: Vocabulary A polyhedron is a three-dimensional solid with flat surfaces and straight edges. Each polygon is a face of the polyhedron. An edge is a segment.](https://reader036.fdocuments.net/reader036/viewer/2022062322/56649f505503460f94c7363a/html5/thumbnails/7.jpg)
Cross Sections
A cross section is the shape formed when a plane intersects a 3D figure.
Think of a very thin slice of the solid.
The bases are opposite faces that are parallel and congruent.
To describe the relationship between the plane and the solid, it will be either: Parallel to the base or Perpendicular to the base
Cross-Sections can be polygons and circles Tell the shape it makes when you cut the solid
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Parallel and Perpendicular Cross Sections
![Page 9: Vocabulary A polyhedron is a three-dimensional solid with flat surfaces and straight edges. Each polygon is a face of the polyhedron. An edge is a segment.](https://reader036.fdocuments.net/reader036/viewer/2022062322/56649f505503460f94c7363a/html5/thumbnails/9.jpg)
A plane slices through the cylinder below, parallel to the base. What is the resulting cross-section?
![Page 10: Vocabulary A polyhedron is a three-dimensional solid with flat surfaces and straight edges. Each polygon is a face of the polyhedron. An edge is a segment.](https://reader036.fdocuments.net/reader036/viewer/2022062322/56649f505503460f94c7363a/html5/thumbnails/10.jpg)
A plane slices through the rectangular prism below, parallel to the base. What is the resulting cross-section?
![Page 11: Vocabulary A polyhedron is a three-dimensional solid with flat surfaces and straight edges. Each polygon is a face of the polyhedron. An edge is a segment.](https://reader036.fdocuments.net/reader036/viewer/2022062322/56649f505503460f94c7363a/html5/thumbnails/11.jpg)
A plane slices through a cone and the resulting cross section is a triangle. Describe the relationship between the plane and the cone.
![Page 12: Vocabulary A polyhedron is a three-dimensional solid with flat surfaces and straight edges. Each polygon is a face of the polyhedron. An edge is a segment.](https://reader036.fdocuments.net/reader036/viewer/2022062322/56649f505503460f94c7363a/html5/thumbnails/12.jpg)
Given a cone with a height of 6 m and a radius of 4 m, what is the area of the cross-section if a plane slices the cone perpendicular to the base, through the center?
6m
4m
![Page 13: Vocabulary A polyhedron is a three-dimensional solid with flat surfaces and straight edges. Each polygon is a face of the polyhedron. An edge is a segment.](https://reader036.fdocuments.net/reader036/viewer/2022062322/56649f505503460f94c7363a/html5/thumbnails/13.jpg)
Find the area of the shaded cross-section of the triangular prism
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A plane intersects a sphere going through the center of the sphere. The radius of the sphere is 5 inches. What is the area of the cross-section, to the nearest tenth?