Question
Stephanie will slice a cylinder into two congruent pieces. Which two-dimensional plane sections could result from the slice Stephanie will make? Select all that apply.
Responses
A pentagonpentagon
B circlecircle
C hexagonhexagon
D rectanglerectangle
E triangle
Responses
A pentagonpentagon
B circlecircle
C hexagonhexagon
D rectanglerectangle
E triangle
Answers
GPT-4o mini
When slicing a cylinder, the resulting two-dimensional plane sections can vary depending on the angle and position of the slice. For a cylinder, there are several possible shapes that can be formed:
- **Circle**: If the slice is made parallel to the bases of the cylinder, the resulting shape will be a circle.
- **Rectangle**: If the slice is made vertically through the side of the cylinder, the resulting shape can be a rectangle.
Shapes like pentagons, hexagons, and triangles are not typically formed from slices of right circular cylinders because they would require cutting at angles or positions that would not produce these shapes.
Therefore, the correct responses are:
- **B**: circle
- **D**: rectangle
- **Circle**: If the slice is made parallel to the bases of the cylinder, the resulting shape will be a circle.
- **Rectangle**: If the slice is made vertically through the side of the cylinder, the resulting shape can be a rectangle.
Shapes like pentagons, hexagons, and triangles are not typically formed from slices of right circular cylinders because they would require cutting at angles or positions that would not produce these shapes.
Therefore, the correct responses are:
- **B**: circle
- **D**: rectangle