Rukasha Maths

GCSE maths Beta

Nets of solids · Revision guide

Foundation · Geometry · 2 pages in the PDF

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Learning objectives

  • Recognise nets that close without overlapping faces.
  • Match face dimensions and connect a cylinder net to circumference.

Key ideas

A net unfolds the surface of a solid. Shared edges become folds; matching edges must fit.

A cube has six equal square faces, but six joined squares are not always a valid net.

A cuboid has three pairs of equal opposite rectangles.

A closed cylinder has two circles and a rectangle of height h and width equal to the circumference.

rectangle width=2πr\text{rectangle width}=2\pi r
A valid cube net with four squares in a row and a square above and below the second; a two-by-three rectangle of squares is marked invalid because faces overlap.

Worked examples

Example 1

List the faces in a net for a 5 cm by 3 cm by 2 cm cuboid.

Each different rectangular face occurs twice.

2 of 5×3,2 of 5×2,2 of 3×22\text{ of }5\times3,\quad2\text{ of }5\times2,\quad2\text{ of }3\times2
6 rectangles in three equal pairs6\text{ rectangles in three equal pairs}

Example 2

A cylinder has radius 3 cm and height 5 cm. Find the dimensions of its rectangular net piece.

The wrapped edge matches the circumference of either circular end.

2πr=2π×3=6π cm2\pi r=2\pi\times3=6\pi\text{ cm}
6π cm×5 cm6\pi\text{ cm}\times5\text{ cm}

Watch out

Check that the net closes without overlap. The wrapped rectangle edge of a cylinder is its circumference, not its diameter.