Developments of solids – sheet-metal patterns of prisms, cylinders and cones
Design & TechnologyEngineering Drawing & DesignAges 15–16
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Sign in to playA sheet-metal blank folded into a prism, a cylinder, an obliquely cut cylinder, a cone or a frustum unfolds strip by strip in 3D; drag the slider to fold it up or lay it flat. Below, a first-angle development drawing shows the front view, the top view divided into 12 parts, projection lines that carry the true lengths of the generators across to the pattern, fold lines, the circumference πD and the radius and angle of the cone's sector.
Lesson: Developments of surfaces: prism, cylinder, cylinder cut at an angle, cone and frustum; true length of generators
What it shows
A development is the flat pattern that folds or rolls into a hollow object, such as a duct, a funnel or a hopper made from sheet metal. Every line in the pattern must have its true length. A cylinder unrolls into a rectangle πD long; when it is cut at an angle, the heights of the 12 generators, true length in the front view, are projected across and give a sine-shaped edge. A cone becomes a sector of radius L = √(R² + H²) and angle φ = 360°·R/L, and a frustum an annular sector.
How to use
Choose a solid and set D, H and, if available, n, α or d. Drag the Unfolded slider, or press Unfold and Fold up, to watch the blank roll into shape. Keep Show true length ticked to see which lines appear at full length in the front view and where they go in the development. Tick Include bases to add the base, the top and the true shape of the oblique cut.
Parameters you can change
- Solid Regular prism, Cylinder, Cylinder cut at an angle, Cone, Frustum of a cone
- Base diameter D (prism: circumscribed circle) 20–120 mm
- Height H (cut cylinder: on the axis) 20–120 mm
- Top diameter d of the frustum 10–110 mm
- Number of sides n of the prism 3–8
- Angle α of the cut plane 0–60 °
- Amount unfolded 0–100 %
- Include bases (and top)
- Highlight true lengths in red
Questions to explore
- Why is the development of a cylinder πD long and not D long?
- In the front view of a cone, which generators appear at their true length?
- How does the curved edge of the cut-cylinder development change when the angle α increases?
