Development (net): surface opened out flat
A development (net) is the outer surface of a 3D object drawn flat so that, folded and joined, it remakes the solid. Every face must be present, true size and next to the face it folds from. A cube is six squares; a prism is its side faces in a row (each width = the matching cross-section edge) plus two end faces; a cylinder is a rectangle of width = circumference (pi x diameter) and height = the cylinder height, plus two end circles. Add glue tabs; fold lines thin.
Cone unrolls to a sector; plot true heights
A cone's curved surface unrolls to a sector: the sector radius is the slant height (the sloping edge, not the vertical height) and the arc length equals the base circumference; the base circle completes the net. A truncation is a straight cut across the solid. On the development the cut edge is not straight: take the true height of each element up from the base line and join the tops (a stepped line or curve). Read true heights off the elevation.
Ellipses are plotted, not sketched
An ellipse has a long major and short minor axis at right angles; its radius varies continuously, so construct it, never freehand. Concentric-circles method: two circles on one centre, radii semi-major and semi-minor; per radial, the outer cut gives a parallel to the minor axis and the inner cut a parallel to the major axis, crossing on the ellipse. Plot 8+ points, join smoothly. Trammel: mark semi-major and semi-minor on a strip, each mark tracking its axis.
Drawn from real examiner reports.
Major and minor axes swapped
A definition trap: the major axis is the longest diameter, the minor the shortest, at right angles. Swapping them builds the ellipse the wrong way round -- tall where it should be wide -- giving each concentric circle the wrong radius. Hold the definitions: outer/larger circle radius = semi-major (long) axis; inner/smaller = semi-minor (short).
Ellipse sketched or too few points
Ellipses are repeatedly the weakest construction. Faults: sketching freehand, too few points so the join is lumpy, mis-orienting the axes, and a trammel used without holding the strip so marks drift. Fix it: concentric circles with 8+ points, outer radius = semi-major and inner = semi-minor; with a trammel, fix the strip and keep each mark on its axis. Finish smoothly.
Digest s23 P53 QA1b; w23 P52/P53 QB4b (Styrofoam block): ellipses were the weakest construction -- sketched freehand, too few points, axes mis-oriented, trammel not attached (s23, w23).
Net missing glue tabs or an adjoining face
On a development candidates omit or mis-place glue flaps and tabs, or leave out an adjoining face, so the net cannot be folded and joined. Every joining edge needs a tab and every face must be present, next to the face it folds from. Before finishing, check each face is there, each fold has its neighbour and each free edge has a tab.
Digest s23 P51 QB5b; s23 P52 QA2: developments lost marks for missing or incorrect glue flaps and tabs and missing adjoining faces (s23).
Fold lines wrong weight or left off
Line conventions carry marks. Fold lines (where faces bend up) must be thin, clearly different from the thick cutting outline round the outside. Common errors: every line the same thick weight, fold lines as a plain solid outline, or left off even when the given start shows the type to continue. Rule: thick = cut edge, thin = fold, tabs on joining edges.
Digest s23 P51 QB5b(i); s23 P52 QA2a: fold-line conventions were widely wrong or absent, and the type shown on the given start was ignored (s23).
Cone sector to vertical, not slant, height
On a cone development the sector radius is the slant height -- the sloping edge -- not the vertical (perpendicular) height. Step off the vertical height and the sector is too small to close. If only the vertical height and base radius are given, find the slant height first (the hypotenuse, longer than the vertical). The arc length must equal the base circumference.
Ellipse struck as compass arcs
A true ellipse's radius changes continuously -- flattest at the major-axis ends, most curved at the minor -- so no single compass radius fits. Joined compass arcs give only a rough oval, not the true curve, and lose marks. Plot points (concentric circles) or trace with a trammel, then join smoothly. A circle has one radius; an ellipse is built from plotted points.
A cylinder net is as wide as the diameter
A testable error: thinking a cylinder's curved surface unrolls to a rectangle as wide as the diameter. It does not -- the width is the distance all the way around, the circumference, which is pi times the diameter. A can 50 mm across unrolls to about 157 mm wide, not 50 mm; the height is the cylinder height and the two end circles are added separately.
Developments: true-size faces, tabs, scale
Work to the stated scale, lay each true-size face next to the one it folds from, make the cylinder rectangle width = circumference plus two end circles, and plot a truncation from true heights, not a flat top. Add tabs; fold lines thin, cut outline thick.
Ellipse: axes right way round, 8+ points
For an ellipse, set the major and minor axes the right way round first, then use concentric circles: outer radius = semi-major, inner = semi-minor, plot 8+ points and join smoothly. Or fix a trammel with both marks on their axes. Show the construction lines.
Copy the line convention on the given start
Line conventions carry their own marks, so copy any convention shown on the given start: continue the fold-line type provided, keep the cut edge thick and fold lines thin, and add a glue tab to every joining edge. Check tabs, fold lines and cut outline before finishing.
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