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Three-Dimensional Figures Study Guide

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Updated on Oct 3, 2011

Introduction to Three-Dimensional Figures

One geometry cannot be more true than another, it can only be more convenient.

—Henri Poincaré (1854–1912)

You have already looked at two-dimensional figures with width and height. Now, you'll look at three-dimensional figures that have a width, height, and depth.

The World You live in is 3-D. When something is three-dimensional, this means that it has depth, width, and height. Look at the objects around you. From your portable Game Boy to your family's car, from a maple tree to lunch, there are many three-dimensional objects that you will cross paths with daily.

A three-dimensional figure is a figure that has depth, width, and height. In other words, it is not flat. There are many different types of three-dimensional figures.

Prisms have flat surfaces, called faces. The faces meet to form edges. The edges meet at corners called vertices. (A single corner is called a vertex.)

Three-Dimensional Figures

Bases are used to name prisms. For example, a rectangular solid, or rectangular prism, is a three-dimensional solid with a rectangle for a base.

Rectangular Solid (prism)

Think of a rectangular solid as being made of rectangles and squares. It has six faces.

A cube is a special type of rectangular solid. In a cube, all the faces are squares.

Cube

A pyramid has a quadrilateral for a base and triangles for sides. It has four triangular faces sharing a common vertex. In other words, a pyramid always comes to a point. Sometimes, the base is also a triangle, which gives the pyramid four faces.

Pyramid

Like a pyramid, a cone is a three-dimensional figure that also comes to a point. It has one circular base and a vertex that is not on the base.

Cone

A sphere is one of the most familiar three-dimensional shapes. It has no flat surfaces. You live on Earth—one large sphere! A sphere is made when you twirl a circle around one of its diameters. Like a circle, all the points of a sphere are at the same distance from its center.

Sphere

A cylinder is a three-dimensional figure that has two parallel, congruent bases. Both bases are circles. If you've seen the stockpiles of canned food at a food drive, you've encountered cylinders.

Cylinder

Find practice problems and solutions for these concepts at Three-Dimensional Figures Practice Questions.

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