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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?
right hexagonal prism
sphere
right triangular prism
right cone

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? $\newline$ right hexagonal prism $\newline$ sphere $\newline$ right triangular prism $\newline$ right cone

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Scale drawings: word problems

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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?

\newline

right hexagonal prism

\newline

sphere

\newline

right triangular prism

\newline

right cone

Consider Solid Shapes: Let's consider each solid and determine if a plane cut parallel to its base could result in a triangular cross section.
Hexagonal Prism: First, we look at the right hexagonal prism. A hexagonal prism has a hexagon for its base. If we cut it with a plane parallel to its base, the cross section would also be a hexagon, not a triangle.
Sphere: Next, we consider the sphere. A sphere does not have a base in the same way a prism does, and any cross section through a sphere is a circle. Therefore, it cannot have a triangular cross section.
Triangular Prism: Now, let's examine the right triangular prism. A triangular prism has a triangle for its base. If we cut it with a plane parallel to its base, the cross section would be the same shape as the base, which is a triangle.
Cone: Finally, we look at the right cone. A cone has a circular base, and a plane cut parallel to its base would result in a circular cross section, not a triangular one.

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