A development is the solid’s surfaces laid flat. To connect the two, list every face of the solid, then give each face its real lengths.
This lesson is part of surface development concepts. The next lesson, tracing corresponding edges, shows how the pieces rejoin.
What is the method?
Use three steps.
- List each face and name its shape.
- Write the real length of every edge.
- Arrange the faces so that the faces touching in the solid stay joined along the shared edge.
Worked example: a triangular prism
An original prism has end faces that are equilateral triangles with side 20 mm. Its length is 50 mm.
Faces. Two equilateral triangles and three rectangles, so five faces.
Lengths. Each rectangle is 20 mm wide, from the triangle side, and 50 mm long. The three rectangles are identical.
Arrangement. Place the three rectangles side by side to form a strip 60 mm wide and 50 mm high. Join one triangle to the top edge of one rectangle and the other to the bottom edge of another, or of the same one.
The strip of three rectangles wraps around the triangle, since 3 × 20 = 60 is the triangle’s perimeter.
Worked example: a cylinder
An original cylinder has diameter 30 mm and height 50 mm.
Faces. One curved surface and two circular ends.
Curved surface. It unrolls into a rectangle 50 mm high. Its length is the circumference: π × 30 ≈ 94.3 mm, using π ≈ 3.142.
Ends. Two circles of diameter 30 mm, each touching the rectangle along one long edge.
The mistake: the diameter as the length
The habit is to draw the rolled-out rectangle 30 mm long, because 30 mm is the number in the question. A rectangle that short would roll into a cylinder that is too thin to fit the end circles.
| Step | Wrong | Right |
|---|---|---|
| Rectangle height | 50 mm | 50 mm |
| Rectangle length | 30 mm (diameter) | 94.3 mm (circumference) |
| Fit to circle | Circle is too large | Rectangle wraps the circle exactly |
The fit check is simple: the rectangle’s long edge must equal the circumference of the circle it touches.
Why the lengths must match
When the development folds up, edges that meet must have the same length. The rectangle’s long edge becomes the rim of the end circle. That shared edge links two faces, so any mismatch leaves a gap or an overlap.
Check yourself
A cylinder has diameter 20 mm and height 40 mm. Give the dimensions of the rolled-out rectangle, using π ≈ 3.142.
Answer
Height is 40 mm. Length is the circumference, π × 20 = 62.84 mm, so about 62.8 mm.
Check: a circle of diameter 20 mm has a rim of 62.8 mm, so the rectangle wraps it exactly.
What to study next
Continue with tracing corresponding edges across a development, then try the development practice set.
If you want a teacher to give you new solids and ask for the face list first, see online one-to-one Engineering Drawing tuition.