QuestionMariko makes a slice through a three-dimensional object perpendicular to the base. The cross-section is a rectangle. What three-dimensional shapes might Mariko have cut? A. Cylinder B. Rectangular prism C. Square pyramid D. Cone
Studdy Solution
STEP 1
1. The slice is perpendicular to the base of the three-dimensional object.
2. The resulting cross-section is a rectangle.
STEP 2
1. Understand the characteristics of the cross-section.
2. Analyze each three-dimensional shape option.
3. Determine which shapes can produce a rectangular cross-section.
STEP 3
Understand that a rectangular cross-section implies that the slice through the object results in a shape with opposite sides equal and all angles .
STEP 4
Analyze each three-dimensional shape option:
- **Cylinder**: A perpendicular slice through a cylinder typically results in a rectangle if the slice is not through the circular base.
- **Rectangular prism**: A perpendicular slice through a rectangular prism can result in a rectangle, depending on the orientation of the slice.
- **Square pyramid**: A perpendicular slice through a square pyramid does not generally result in a rectangle; it usually results in a trapezoid or triangle.
- **Cone**: A perpendicular slice through a cone does not result in a rectangle; it typically results in a triangle or a sector of a circle.
STEP 5
Determine which shapes can produce a rectangular cross-section:
- **Cylinder**: Yes, it can produce a rectangular cross-section.
- **Rectangular prism**: Yes, it can produce a rectangular cross-section.
- **Square pyramid**: No, it cannot produce a rectangular cross-section.
- **Cone**: No, it cannot produce a rectangular cross-section.
The three-dimensional shapes that might have been cut to produce a rectangular cross-section are:
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