Question
A solid is cut by a plane that is parallel to its base, forming a two-dimensional cross section in the shape of a hexagon. Which of the following solids could have resulted in that cross section?
Answer
Multiple Choice Answers
spheresphere
right hexagonal prismright hexagonal prism
right pentagonal prismright pentagonal prism
rectangular prismrectangular prism
Answer
Multiple Choice Answers
spheresphere
right hexagonal prismright hexagonal prism
right pentagonal prismright pentagonal prism
rectangular prismrectangular prism
Answers
GPT-4o mini
To determine which solid could have a hexagonal cross section when cut by a plane parallel to its base, we can consider the characteristics of each option:
1. **Sphere**: A sphere has no edges or flat surfaces, so it cannot produce a hexagonal cross section.
2. **Right Hexagonal Prism**: A right hexagonal prism has hexagonal bases and vertical edges connecting the bases. If a plane is cut parallel to the hexagonal base, it will result in a hexagonal cross section, matching the base shape.
3. **Right Pentagonal Prism**: A right pentagonal prism has pentagonal bases. If a plane is cut parallel to the base, the cross-section will also be pentagonal, not hexagonal.
4. **Rectangular Prism**: A rectangular prism has rectangular bases. A plane cut parallel to the base will produce a rectangular cross section, not a hexagonal one.
Based on this analysis, the solid that could produce a hexagonal cross section when cut by a plane parallel to its base is the **right hexagonal prism**.
1. **Sphere**: A sphere has no edges or flat surfaces, so it cannot produce a hexagonal cross section.
2. **Right Hexagonal Prism**: A right hexagonal prism has hexagonal bases and vertical edges connecting the bases. If a plane is cut parallel to the hexagonal base, it will result in a hexagonal cross section, matching the base shape.
3. **Right Pentagonal Prism**: A right pentagonal prism has pentagonal bases. If a plane is cut parallel to the base, the cross-section will also be pentagonal, not hexagonal.
4. **Rectangular Prism**: A rectangular prism has rectangular bases. A plane cut parallel to the base will produce a rectangular cross section, not a hexagonal one.
Based on this analysis, the solid that could produce a hexagonal cross section when cut by a plane parallel to its base is the **right hexagonal prism**.