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A solid is cut by a plane that is parallel to its base, forming a two-dimensional cross section in the shape of a triangle. Which of the following solids could have resulted in that cross section?
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Q. A solid is cut by a plane that is parallel to its base, forming a two-dimensional cross section in the shape of a triangle. Which of the following solids could have resulted in that cross section?
- Identify characteristics: Identify the characteristics of the cross section. The cross section is a triangle, which means the solid must have a base that can allow for a triangular cross section when cut by a plane parallel to it.
- Consider triangular base: Consider solids with a triangular base. Solids like a triangular pyramid (tetrahedron) have triangular bases. When cut by a plane parallel to the base, these solids would result in a triangular cross section.
- Consider polygonal base: Consider solids with a polygonal base that can have triangular cross sections.A prism with a polygonal base can also have a triangular cross section if the plane cuts through the solid in a way that intersects three non-adjacent vertices.
- Consider circular bases: Consider solids with circular bases.Solids with circular bases, such as cylinders or cones, cannot have a triangular cross section because a plane parallel to the base would result in a circular or elliptical cross section.
- Determine possible solids: Determine the possible solids.Based on the above reasoning, the possible solids that could have a triangular cross section when cut by a plane parallel to its base are a triangular pyramid or a prism with a polygonal base that allows for such a cross section.
