Cross-Sections

The cross-section of an object is the face that would remain if we were to cut cleanly through it. The horizontal cross-section of a right prism or cylinder is the same shape and size as its base. Right prisms and cylinders have the same horizontal cross-section all along their height.

Cross Section of Prism

The horizontal cross-section of a pyramid is a similar figure to its base. If a horizontal cut is made toward the top of the pyramid, the cross-section will be smaller than a cross-section toward the bottom of the pyramid, as shown in the picture below.

Cross Section of Pyramid

If the cross-section is oblique, then the shape may or may not be congruent or similar to the base of the solid.  In the drawing below, the cone has a horizontal cross section that creates a circle but the oblique cross-section creates an ellipse.

Cross Section of Cone

 

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