Question

A solid is cut by a plane that is perpendicular to its base, forming a two-dimensional cross section in the shape of a triangle. Which of the following solids could have resulted in that cross section?
Answer
A. right coneright cone
B. spheresphere
C. right hexagonal prismright hexagonal prism
D. right pentagonal prismright pentagonal prism

Answer 1

To determine which of the given solids could result in a triangular cross-section when cut by a plane perpendicular to its base, let's analyze each option:

A. **Right Cone**
- A right cone has a circular base and, when sliced with a plane perpendicular to the base, can generate a triangular cross-section. As you move up the height of the cone, the intersection can vary, but if the plane is placed properly, you can indeed get a triangular shape.

B. **Sphere**
- Slicing a sphere with a plane perpendicular to any base doesn't produce a triangular cross-section. A sphere cut will always yield circular sections regardless of the plane's orientation.

C. **Right Hexagonal Prism**
- A right hexagonal prism has a hexagonal base. If cut perpendicularly to the base, the cross-section would also be a hexagon, therefore not able to produce a triangular cross-section.

D. **Right Pentagonal Prism**
- A right pentagonal prism has a pentagonal base. Similar to the hexagonal prism, cutting it perpendicularly will yield a pentagonal cross-section, not a triangular one.

Based on this analysis, the only solid that can result in a triangular cross-section when cut by a plane perpendicular to its base is:

**A. Right Cone**