Objects look different from alternate points of view. If you toss around a cube, you see that it is three-dimensional. But suppose the cube is on a table and you are staring directly down at it. In this case it would just look like a square. In this Cyberchase interactive activity, each member of the CyberSquad is standing in a different place, but they are all looking at the same arrangement of blocks. The challenge is to figure out exactly what each member sees from his or her point of view.
Download and ShareA plane figure is a two-dimensional figure which lies in one plane. A plane figure has only two dimensions, length and width. Examples of plane figures include rectangles, triangles, and circles. Plane figures have an area and a perimeter, but they do not have a volume, since they do not occupy a three-dimensional space.
A solid is a three-dimensional figure that has length, width, and depth. These objects also have a volume, which is the measure of the space they occupy. The faces of a solid are made up of various two-dimensional figures. For example, the faces of a cube are all squares, while the outer surface of a cylinder consists of two circles and a rectangle.
Because a three-dimensional solid is comprised of two-dimensional faces, it is possible that it will look different depending on the position from which it is viewed. If you consider an ancient pyramid, flying directly above the structure would make the pyramid appear to look like a square. On the other hand, if you are standing a distance away from the pyramid, the side of the pyramid will look like a triangle. Therefore, it is important to consider what an object looks like from the top, bottom, and all sides in order to accurately describe its shape.
Sometimes it can be helpful to consider only two dimensions of a three-dimensional object. For instance, if you are arranging rectangular tables in a cafeteria, you need to know how much floor space each table covers. It is not necessary to consider the height of the tables. You can take the cafeteria floor as the plane, and imagine you are looking down from above. It would appear as though the table tops are resting flat on the floor. Since you're dealing with rectangles, you can draw all possible table arrangements right on a piece of paper.
In technical drawing, or drafting, a similar process takes place. In this case, a drafter describes a three-dimensional model by using a collection of two-dimensional images. These images are the views of the object from various perspectives. Drafters can create blueprints for objects such as buildings, toys, electronics, and highways. Computer Aided Design (CAD) software has been developed to aid in this design process. CAD systems allow an engineer to easily view a design from any angle. They can also zoom-in to get a more detailed view.
To learn more about three-dimensional shapes, check out Identifying 2-D and 3-D Shapes in Crystals and Making Rock Candy.
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