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?
Question
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?
Solution
The solids that could have resulted in a triangular cross section when cut by a plane parallel to its base include a pyramid, a cone, or a prism with a triangular base.
Step 1: Consider the shape of the cross section, which is a triangle. Step 2: Think about which three-dimensional shapes would result in a triangular cross section when cut parallel to their base. Step 3: Conclude that a pyramid, a cone, or a prism with a triangular base would all result in a triangular cross section when cut in this way.
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