How to Analyze Cross Sections of 3D Solids: A Step-by-Step Guide

Examples

Practice Questions:

1. What will be the shape of a cross-section if a cone is sliced horizontally near its base?
2. If a pyramid with a square base is sectioned parallel to its base halfway up, what shape will the cross-section reveal?
3. What is the shape of the cross-section when a cylinder is cut at an angle, not parallel to its base or directly vertical?
4. If a cube has an edge length of \(6 \text{ cm}\) and is sliced parallel to one of its faces, but only \(2 \text{ cm}\) from the face, what is the area of the resulting cross-section?
5. What will be the shape of a cross-section if a triangular pyramid is sliced horizontally near its apex?
6. When a cone is cut horizontally close to its tip, what shape does the cross-section reveal, and how does it relate to the base of the cone?

1. A smaller circle.
2. A smaller square.
3. An ellipse.
4. \( 36 \text{ cm}^2 \) (It’s a square with the same edge length as the cube).
5. A smaller triangle.
6. A circle, much smaller than the base.