What shape results from the revolution of a circle along a line?

What shape results from the revolution of a circle along a line?

• A. Sphere
• B. Cylinder
• C. Torus
• D. Cone

Answer: (C)

When a circle revolves around a line that lies in the same plane as the circle but does not intersect it, the resulting shape is known as a torus. This occurs because the circular path creates a three-dimensional shape that resembles a donut, characterized by a hole in the middle. In contrast, if the circle were to revolve around an axis that goes through its center, it would create a sphere. If the circle revolved around a line that is not in its plane but intersects it, a cone would be formed. Lastly, revolving the circle around an axis that is parallel to it and outside of it leads to the creation of a cylinder. Understanding these geometric transformations is essential in visualizing how shapes interact in three-dimensional space.

When a circle revolves around a line that lies in the same plane as the circle but does not intersect it, the resulting shape is known as a torus. This occurs because the circular path creates a three-dimensional shape that resembles a donut, characterized by a hole in the middle.

In contrast, if the circle were to revolve around an axis that goes through its center, it would create a sphere. If the circle revolved around a line that is not in its plane but intersects it, a cone would be formed. Lastly, revolving the circle around an axis that is parallel to it and outside of it leads to the creation of a cylinder. Understanding these geometric transformations is essential in visualizing how shapes interact in three-dimensional space.