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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?

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 rectangle. Which of the following solids could have resulted in that cross section?

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Solution

The solids that could have resulted in a rectangular cross section when cut by a plane perpendicular to its base include a cylinder, a rectangular prism, or a cube.

Here's why:

  1. Cylinder: If a cylinder is cut perpendicular to its base, the cross section would be a circle. However, if the cylinder is very elongated (more like a pipe), the cross section could appear to be a rectangle, especially if the cut is not perfectly perpendicular.

  2. Rectangular Prism: A rectangular prism has a rectangular base and if cut perpendicular to its base, it would result in a rectangular cross section.

  3. Cube: A cube is a special type of rectangular prism where all faces are squares. If a cube is cut perpendicular to its base, the cross section would be a square, which is a special type of rectangle.

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