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Ms. D's Chapter 10 - Spatial Reasoning
3-D Solid Geometry Class Notes PDF Print E-mail

Three-dimensional figures can be made up of flat or curved surfaces.  Prisms and pyramids are named by the shapes of their bases.

A flat surface is called a face.  An edge is the intersection of two faces.  A vertex is the intersection of three or more faces.

A net is a diagram of the surfaces of a three-dimensional figure that can be folded to form the three-dimensional figure.

The net at the right has one rectangular face.  The remaining faces are triangles.  The net forms a rectangular pyramid.

A cross-section is the intersection of a three-dimensional figure and a plane.

Since the figure on the left is a rectangular pyramid, the cross section is a rectangle.

An isometric drawing is drawn on isometric dot paper and shows three sides of a figure from a corner view.  A solid and an isometric drawing of the solid are shown in the image on the right.

Orthographic views show three-dimensional objects from six different perspectives.

Top: Picture yourself above the figure and looking straight down.

Front: Choose one side of the figure to be the front.  Visualize looking straight at the figure.

Right: Picture walking around to the right side of the figure and looking straight at it.

Bottom: Picture yourself directly underneath the figure and looking straight up.

Left: Picture walking around the corner to the left side of the figure and looking straight at it.

Back: Picture walking around to the back of the figure and looking straight at it.

Perspective Drawings

A perspective drawing shows parallel lines drawn such that they meet at a vanishing point.  In a one-point perspective drawing, nonvertical lines are drawn so that they meet at a vanishing point.

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Chapter 10 Letter to Parents PDF Print E-mail

In this chapter, your child will learn about three-dimensional figures and special relationships. Your child will then learn to determine the surface areas and volumes of these three-dimensional figures.

 

Your child will begin the lesson with a look at solid geometry. There are four basic three-dimensional figures at which your child will be looking – prism, pyramid, cylinder, and cone. Your child will learn more about these figures by using a net. A net is a diagram of a three-dimensional figure that can be folded to form the three-dimensional figure.

 

Your child will also use formulas for these three-dimensional figures. One conjecture that your child will have to make is about the relationships between the vertices, edges, and faces of a polyhedron. A polyhedron is formed by four or more polygons that intersect only at their edges. Euler’s Formula says that for any polyhedron with V vertices, E edges, and F faces,

V - E + F = 2

 

Your child will then move on to determine the surface areas and volumes of different figures. It will be helpful to use the net of the figure to do this.

 

The surface area of a figure is different from the lateral area. The surface area is the total area of all faces and curved surfaces of a three-dimensional figure. The lateral area of a figure is the sum of the areas of the lateral faces. The lateral face is a face of a prism or pyramid that is not a base.

 

Your child will also learn about the unique shape of spheres. A sphere is the locus of points in space that are a fixed distance from a given point called the center of a sphere. The radius of a sphere connects the center of the sphere to any point on the sphere.

 

Please open the attached PDF to read the entire letter which includes the formula chart.

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Chapter 10 Videos from Textbook PDF Print E-mail

Click on the links to watch short tutorials and take interactive quizzes:


* 10-2 Representations of 3D Figures, pp. 661 - 668
video #1
, video #2, video #3, video #4Interactivity, Practice Quiz 10-2
 
* 10-1 Identifying 3D Figures from Nets, pp. 654 - 660
video #1
, video #2, video #3, video #4, Practice Quiz 10-1

 
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