Development of Surfaces
Development questions test whether you can unroll a solid surface to a flat sheet without stretching it.
Methods
Parallel-line development is used for prisms and cylinders: stretch the perimeter along a line and set off the true height. Radial-line development is used for pyramids and cones: use the true slant length as radius and step the base divisions around an arc. Triangulation is used for oblique solids and transition pieces. For a cone, the sector angle is (base radius / slant height) × 360°. For a truncated solid, project the true lengths of the cut edges before setting them out.
Worked example
A cylinder has a 50 mm diameter and 80 mm height. The circumference is π × 50 = 157.1 mm. The development is a rectangle 157.1 mm × 80 mm, divided into 12 equal parts to match the circle. Reasoning: the lateral surface unrolls without stretching, so its width equals the circumference, not the diameter. Add a seam allowance only if the question asks for it.
Traps
Using the diameter instead of the circumference; using the axial height of a cone instead of its slant height; forgetting to divide the circle into equal parts; not transferring the true lengths of a truncated edge; adding an allowance that was not asked for.