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Introduction to 3D Figures

This topic covers the identification of various three-dimensional figures. Sketching of cross sections of three-dimensional figures is also covered.

Topic: Prisms and Pyramids

  • Three-dimensional figures have three dimensions: length, width, and height

  • A flat surface of a three-dimensional figure is a face

  • A polyhedron is a three-dimensional figure whose faces are all polygons. The face that is used to name a polyhedron is called a base

  • A prism is a polyhedron that has two parallel, congruent bases. The bases can be any polygons. The other faces are parallelograms

  • A pyramid is a polyhedron that has one base. The base can be any polygon. The other faces are triangles

Topic: Cylinders, Cones, and Spheres

  • A flat surface of a three-dimensional figure is a face

  • A polyhedron is a three-dimensional figure whose faces are all polygons. The face that is used to name a polyhedron is called a base

  • A cylinder has two, parallel bases that are circles

  • A cone has one base that is a circle and a surface that comes to a point called the vertex

  • A sphere is a figure which has no flat surface. Any point on its surface is equidistant from a point called the center

Topic: Three-Dimensional Figures from Different Views

  • Identify the top, front, and side of the figure

  • Sketch each side as it looks when you look at it directly

  • View the figure from the front, top, and side and draw what you see

Topic: Identify Cross Sections

  • When a three-dimensional figure and a plane intersect, the intersection is called a cross section

  • A three-dimensional figure can have many different cross sections. The cross section depends on the direction of cut

  • Any cross section that is made by cutting a figure parallel to the base will be like the shape of the base

Topic: Three-Dimensional Figures Formed by Transformations

  • When a three-dimensional figure and a plane intersect, the intersection is called a cross section

  • Three-dimensional figures can be formed by translating or rotating a cross section through space
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