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 circle. Which of the following solids could have resulted in that cross section?
Answer
Multiple Choice Answers
right cylinderright cylinder
right hexagonal prismright hexagonal prism
rectangular pyramidrectangular pyramid
right triangular prismright triangular prism
Answer
Multiple Choice Answers
right cylinderright cylinder
right hexagonal prismright hexagonal prism
rectangular pyramidrectangular pyramid
right triangular prismright triangular prism
Answers
GPT-4o mini
To determine which solid could result in a circular cross section when cut by a plane parallel to its base, let's analyze each option:
1. **Right Cylinder**: A right cylinder has circular bases, and a plane parallel to the bases will result in a circular cross section. So this is a valid choice.
2. **Right Hexagonal Prism**: A right hexagonal prism has hexagonal bases. A plane parallel to the bases would create a hexagonal cross section, not circular. Thus, this is not a valid choice.
3. **Rectangular Pyramid**: A rectangular pyramid has a rectangular base and can produce various cross sections depending on the cut. However, a cut parallel to the base would yield a smaller rectangle, not a circle. Therefore, this is not a valid choice.
4. **Right Triangular Prism**: A right triangular prism has triangular bases. A plane parallel to the bases would yield a triangular cross section, not a circle. Thus, this is not a valid choice.
Based on the analysis, the only solid that can produce a circular cross section when cut by a plane parallel to its base is the **right cylinder**.
1. **Right Cylinder**: A right cylinder has circular bases, and a plane parallel to the bases will result in a circular cross section. So this is a valid choice.
2. **Right Hexagonal Prism**: A right hexagonal prism has hexagonal bases. A plane parallel to the bases would create a hexagonal cross section, not circular. Thus, this is not a valid choice.
3. **Rectangular Pyramid**: A rectangular pyramid has a rectangular base and can produce various cross sections depending on the cut. However, a cut parallel to the base would yield a smaller rectangle, not a circle. Therefore, this is not a valid choice.
4. **Right Triangular Prism**: A right triangular prism has triangular bases. A plane parallel to the bases would yield a triangular cross section, not a circle. Thus, this is not a valid choice.
Based on the analysis, the only solid that can produce a circular cross section when cut by a plane parallel to its base is the **right cylinder**.