Sections of Solids and True Shapes

Sections of Solids and True Shapes

Cut a solid with a plane and the exposed face is the section. If the cutting plane is inclined, that face appears foreshortened in the standard views — so its true shape must be projected separately, exactly as with an auxiliary view.

The method is ordered and must not be shortcut:

1. Draw the elevation and plan of the uncut solid.
2. Draw the cutting plane on the view where it appears as a line.
3. Mark every point where the cutting plane crosses an edge of the solid, and number them.
4. Project each numbered point into the other view.
5. Project all points perpendicular to the cutting plane, transfer the widths from the plan, and join in order.

Worked example. A cylinder cut at 45° gives an ellipse. A cylinder cut square across gives a circle. A cone cut parallel to its slant gives a parabola. The solid did not change — only the angle of the cut did.

Core checkpoint: Number the intersection points and project them in order. Joining points out of order produces a crossed, self-intersecting outline.