Cylinders and Cones

≈ 38 min

Cylinders and Cones

Curved solids need one extra idea: because they have no edges to project, you work with generators — a set of imaginary straight lines along the surface, evenly spaced.

A cylinder with its axis perpendicular to the HP gives a circle in plan and a rectangle in elevation. A cone gives a circle in plan with lines to the centre, and a triangle in elevation.

Generators are what make curved solids solvable. Divide the plan circle into 12 equal parts and project each division up into the elevation. Each becomes a straight line on the surface — and straight lines can be intersected, measured and transferred, which curves cannot.

True lengths on a cone. Every generator of a right cone is the same length, and it appears true length only when it lies parallel to the VP — that is, on the extreme left or right outline of the elevation. So one measurement off the outline gives the true length of all generators.

Worked example. To find where a cutting plane crosses a cone, mark where the plane crosses each of the 12 generators in the elevation, project each point down to its own generator in the plan, and join. A curve found point by point along generators, never sketched.

Core checkpoint: Divide, project, work generator by generator, then join. Never sketch a curve through guessed points.

What name is given to the evenly spaced straight lines drawn along the surface of a cone or cylinder to make it solvable?

Which generators of a right cone appear at true length in the elevation?

Only those on the extreme left and right outline, because they are parallel to the VP.

All of them, because every generator of a right cone is the same length.

Only the one nearest the viewer.

None — true length must always be found by rotation.

Why are generators used rather than working with the curved surface directly?

Straight lines can be intersected, measured and transferred between views; curves cannot be handled that way point by point.

Because curves cannot be drawn with instruments.

Because generators make the drawing look more detailed.

Because a cone has no curved surface.

To find where a cutting plane crosses a cone, what is the correct procedure?

Mark where the plane crosses each generator in the elevation, project each point onto its own generator in the plan, and join the results.

Sketch a smooth curve where the plane appears to cut the outline.

Measure the plane's angle and calculate the curve.

Project only the two outline generators and join them.