Cylinder
SŠ10 minProjections of a cylinder and its outline.
Solid
A is the base centre and the radius reaches the farthest of the remaining points in plan. The circle is approximated by an n-gon – exactly as on paper.
Points · 2
max 12The radius reaches the farthest point. For a base with any number of vertices, switch to Prism.
Planar section
3D view
Perspective
Bring the eye closer and parallel edges rush together toward a vanishing point; move it away and perspective tends to parallel projection.
Measurements
- Volume
- 107.46
- Surface
- 144.24
- Vertices V
- 48
- Edges E
- 72
- Faces F
- 26
- V − E + F
- 2
V − E + F = 2 holds for every simple polyhedron (Euler’s formula) – a quick check that the body is closed.
Theory
A cylinder of revolution is generated by rotating a segment – a generating line – about an axis. In Monge projection we fix it by base and height: the base is a circle lying in the projection plane, with the axis perpendicular to it.
With a vertical axis the top view is the base circle in true size and the front view is a rectangle as wide as the diameter and as tall as the cylinder. Its vertical sides are the projections of the outermost generating lines.
The outline is not an edge of the solid – it is where the line of sight merely grazes the surface. So it changes with the direction of projection: tilt the axis and the base circle becomes an ellipse.
Step-by-step construction
Practice
Build the construction yourself
What is the next step?
1 / 6Choose the step that comes next. The drawing only advances on a correct choice.
Check your understanding
What is the top view of a cylinder with a vertical axis?
What forms the outline of the cylinder in the front view?
How does the projected base change when the axis is tilted?
Downloadable material
A PDF for this lesson is in preparation.
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