A solid is cut by a plane that is perpendicular 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?
Question
A solid is cut by a plane that is perpendicular 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?
Solution
The solids that could have resulted in a triangular cross section when cut by a plane perpendicular to its base include a pyramid, a cone, or a prism.
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Pyramid: A pyramid has a polygonal base and triangular faces that converge to a single point. If a pyramid is cut perpendicular to its base, the cross section would be a triangle.
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Cone: A cone has a circular base and a curved surface that converges to a single point. If a cone is cut perpendicular to its base, the cross section would be a triangle.
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Prism: A prism has two parallel polygonal bases and rectangular faces. If a triangular prism is cut perpendicular to its base, the cross section would be a triangle.
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