A diagonal cross section of a sphere produces which two-dimensional shape?
The Correct Answer and Explanation is:
A diagonal cross section of a sphere produces a circle.
To understand this, we need to recall the geometry of a sphere. A sphere is a three-dimensional object where every point on its surface is equidistant from a central point (the center of the sphere). When you slice through the sphere with a plane, the resulting cross section can produce different shapes depending on how the plane intersects the sphere.
- If the plane cuts through the center of the sphere (i.e., through its diameter), the cross section will be a circle. This is the largest possible circular cross section, and the diameter of the circle will be equal to the diameter of the sphere.
- If the plane cuts parallel to a tangent of the sphere (at any point other than the center), the resulting cross section will be a smaller circle or, in extreme cases, a single point if the plane just touches the surface of the sphere.
Now, when we talk about a diagonal cross section, we are imagining a plane slicing through the sphere at an angle, not necessarily along a horizontal or vertical axis. If this plane intersects the center of the sphere, it will still produce a circle, just oriented at an angle relative to a traditional coordinate plane. The size of the circle will depend on the position of the plane, but it will always be a circle, regardless of the angle of the slice.
In summary, regardless of how you slice the sphere (as long as it cuts through its center or any other part of the surface), the resulting two-dimensional shape is always a circle.
