A proposed net is checked in two steps: count the faces against the solid, then compare the lengths that must meet. Passing only one of the two is not enough.
This lesson is in surface development concepts. It uses the matching idea from tracing corresponding edges.
What does each check find?
The face count finds missing or extra faces. The length match finds edges that cannot meet, even when every face is present.
Worked example: a closed rectangular prism
An original closed prism is 40 mm long, 30 mm wide and 20 mm high. A student proposes a net made of five rectangles: 40 × 30, 40 × 20, 40 × 20, 30 × 20 and 30 × 20.
Count. A closed rectangular prism has six faces in three pairs: two of 40 × 30, two of 40 × 20 and two of 30 × 20.
Compare. The net has only one 40 × 30 rectangle. The second 40 × 30, the lid, is missing.
So the net is an open box until a lid is added.
Worked example: a cylinder net that fails on length
An original cylinder has diameter 14 mm and height 30 mm. A student draws a rectangle 30 mm high and 40 mm long, with two circles of diameter 14 mm attached.
Count. One rectangle and two circles make three faces. That matches a cylinder.
Length. The circumference is π × 14 ≈ 44 mm. The rectangle is 40 mm long, which is 4 mm short of the rim.
When folded, the rectangle cannot wrap around the circle. A correct rectangle is 30 mm high and about 44 mm long.
The mistake: stopping after the count
The count is quick and feels decisive. A student who counts three faces for the cylinder concludes the net is fine and never compares lengths.
| Check | Cylinder net | Verdict |
|---|---|---|
| Face count | 3, as required | Pass |
| Length match | 40 mm against 44 mm | Fail |
| Overall | Does not fold | Fail |
A net passes only when every check passes. A count that matches can still hide a fault.
Using the order
Do the count first, because it is faster and any missing face changes the picture. Then compare lengths pair by pair, following the corners as in the previous lesson.
Check yourself
A cube has edge 25 mm. A cross-shaped net has five squares of side 25 mm and a sixth square of side 20 mm at the end. Which check catches the fault?
Answer
The count passes: six squares for six faces. The length check fails: the sixth square’s edges are 20 mm, but the edges it must meet are 25 mm.
The repair is to make the sixth square 25 mm × 25 mm.
What to study next
Go on to explaining an original development choice geometrically and then test your two checks in the development practice set.
If you want a teacher to give you nets with hidden faults, see online one-to-one Engineering Drawing tuition.