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