To determine which three-dimensional object is formed when a circle is continuously rotated about its diameter, let's break down the concept step-by-step:
1. Understanding the Circle Rotation:
- A circle is a two-dimensional shape that has a set of all points in a plane that are at a given distance (radius) from a given point (center).
- When this circle is rotated, it means every point on the circle follows a circular path around the axis of rotation.
2. Axis of Rotation:
- The diameter of the circle is being used as the axis of rotation. The diameter is a straight line passing from side to side through the center of a circle.
3. Effect of Rotation:
- If you rotate the circle about its diameter, each point on the circle traces out a circular arc.
- Essentially, every point on the circumference of the circle will rotate around the diameter, sweeping out a three-dimensional space.
4. Resulting 3D Object:
- When the circle rotates 360 degrees around its diameter, the surface traced out by the circle is a sphere.
A sphere is defined as the set of all points in three-dimensional space that are at a given distance (the radius) from a given point (the center).
Thus, the three-dimensional object formed by continuously rotating a circle about its diameter is:
(3) Sphere
