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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 rectangle. Which of the following solids could have resulted in that cross section? rectangular pyramid sphere rectangular prism right cone

A solid is cut by a plane that is perpendicular to its base, forming a two-dimensional cross section in the shape of a rectangle. Which of the following solids could have resulted in that cross section?\newlinerectangular pyramid\newlinesphere\newlinerectangular prism\newlineright cone

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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 rectangle. Which of the following solids could have resulted in that cross section?\newlinerectangular pyramid\newlinesphere\newlinerectangular prism\newlineright cone
  1. Identify characteristics: Identify the characteristics of the cross section. A rectangle has four sides with opposite sides being equal and parallel, and it has four right angles. This means that the solid must have a flat surface parallel to the base to create such a cross section when cut perpendicularly.
  2. Analyze rectangular pyramid: Analyze the first option: a rectangular pyramid. A pyramid has triangular sides that converge to a single point. If you cut a pyramid with a plane perpendicular to its base, you cannot get a rectangle because the sides are not parallel and do not form right angles.
  3. Analyze sphere: Analyze the second option: a sphere. A sphere has no flat surfaces, and any cross section through a sphere is a circle or an ellipse, not a rectangle.
  4. Analyze rectangular prism: Analyze the third option: a rectangular prism. A rectangular prism has flat faces and a rectangular base. If you cut a rectangular prism with a plane perpendicular to its base, you can indeed get a rectangular cross section because the sides of the prism are parallel and form right angles.
  5. Analyze right cone: Analyze the fourth option: a right cone. A cone has a circular base and a single curved surface that tapers to a point. A cross section perpendicular to the base of a cone would be a circle, not a rectangle.

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