Question
The two cross sections shown resulted from the intersection of two planes parallel to the base of a solid. Which could be the solid?
image
A
a cube
B
a rectangular prism
C
a square pyramid
D
a sphere
Answers
GPT-4o mini
To determine which solid could result in the given cross sections, we need to analyze the features of the provided cross sections. Given that the intersection of two planes is parallel to the base of the solid, we can infer the following characteristics for each solid option:
A. **Cube** - A cube will have cross sections that could be squares at varying heights, since all sides are equal and all faces are squares.
B. **Rectangular Prism** - Similar to the cube, a rectangular prism can have rectangular cross sections, which can vary in size depending on the height, and the cross sections taken parallel to the base will also be rectangles.
C. **Square Pyramid** - A square pyramid will have cross sections parallel to the base that are squares, but as you move up the height, these squares will decrease in size, becoming smaller as you approach the apex.
D. **Sphere** - A sphere will have circular cross sections that remain constant in size up to the equator, and the cross sections will change to smaller circles as you move above and below that equatorial region.
Without seeing the actual image, I can't definitively determine which solid's cross sections match. However, if the given cross sections are squares or rectangles, this could fit either the cube or rectangular prism. If the cross sections are circular, this would fit the sphere. If the sections taper, it would fit the square pyramid.
Please refer to the specific shapes of the cross sections in the image to conclude which solid is the correct answer.
A. **Cube** - A cube will have cross sections that could be squares at varying heights, since all sides are equal and all faces are squares.
B. **Rectangular Prism** - Similar to the cube, a rectangular prism can have rectangular cross sections, which can vary in size depending on the height, and the cross sections taken parallel to the base will also be rectangles.
C. **Square Pyramid** - A square pyramid will have cross sections parallel to the base that are squares, but as you move up the height, these squares will decrease in size, becoming smaller as you approach the apex.
D. **Sphere** - A sphere will have circular cross sections that remain constant in size up to the equator, and the cross sections will change to smaller circles as you move above and below that equatorial region.
Without seeing the actual image, I can't definitively determine which solid's cross sections match. However, if the given cross sections are squares or rectangles, this could fit either the cube or rectangular prism. If the cross sections are circular, this would fit the sphere. If the sections taper, it would fit the square pyramid.
Please refer to the specific shapes of the cross sections in the image to conclude which solid is the correct answer.