When a cone is sliced by a plane parallel to its base, but not passing through its apex, what is the shape of the resulting cross-section?
- A
- B
- C
- D
Solution & Step-by-step Explanation
According to the properties of conic sections:
1. When a right circular cone is cut by a plane parallel to its circular base, the intersection forms a Circle.
2. If the plane is tilted slightly (not parallel to the base) but cuts through all generators, it forms an ellipse.
3. If the plane is parallel to the generator side, it forms a parabola.
4. If the plane is parallel to the central axis, it forms a hyperbola.
Since the cutting plane is specified as parallel to the base, the resulting cross-section is a circle.
1. When a right circular cone is cut by a plane parallel to its circular base, the intersection forms a Circle.
2. If the plane is tilted slightly (not parallel to the base) but cuts through all generators, it forms an ellipse.
3. If the plane is parallel to the generator side, it forms a parabola.
4. If the plane is parallel to the central axis, it forms a hyperbola.
Since the cutting plane is specified as parallel to the base, the resulting cross-section is a circle.