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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? triangular pyramid right pentagonal prism right triangular prism sphere

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?\newlinetriangular pyramid\newlineright pentagonal prism\newlineright triangular prism\newlinesphere

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Q. 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?\newlinetriangular pyramid\newlineright pentagonal prism\newlineright triangular prism\newlinesphere
  1. Identify characteristics: Identify the characteristics of the cross section. The cross section is a triangle, which means the solid must have a triangular face that can be exposed by such a cut.
  2. Analyze triangular pyramid: Analyze the first option: a triangular pyramid. A triangular pyramid has triangular faces. If a plane cuts perpendicular to the base of a triangular pyramid, it could reveal a triangular cross section.
  3. Analyze pentagonal prism: Analyze the second option: a right pentagonal prism. A right pentagonal prism has rectangular faces and two pentagonal bases. A cut perpendicular to the base would reveal a pentagonal cross section, not a triangular one.
  4. Analyze triangular prism: Analyze the third option: a right triangular prism. A right triangular prism has rectangular faces and two triangular bases. A cut perpendicular to the base would reveal a triangular cross section.
  5. Analyze sphere: Analyze the fourth option: a sphere. A sphere does not have flat faces. Any plane cut through a sphere would result in a circular cross section, not a triangular one.
  6. Determine possible solids: Determine which solids could result in a triangular cross section. Both the triangular pyramid and the right triangular prism have triangular bases, so both could result in a triangular cross section when cut by a plane perpendicular to their bases.

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