Nets of Solids (Edexcel IGCSE Maths)

Nets of solids

What is a net of a solid?

• A net of a solid is a 2D drawing that can be cut out and folded to make a 3D shape

• Each of the faces of the 3D shape are arranged in a certain pattern

  • Not every arrangement of the faces will create a net of that solid
  • Solids can have more than one arrangement that will work to make the 3D shape

• The area of the net of a 3D shape is the same as the surface area of the solid

Nets of solids

What does the net of a cube or cuboid look like?

• The net of a cube has 6 squares connected at certain edges
• There are 11 different arrangements of the square faces that will form a net of a cube

• The most common and easiest to remember is in the form of a cross

• A cuboid has 6 rectangular faces, so its net consists of 6 rectangles

• The rectangles will be in three pairs of two

• There are 54 different possible nets of a cuboid

  • Again, the most common and easiest to remember is in the form of a cross

  • Pay attention to which rectangles are the same

    • They are colour-coded in the diagram below

What does the net of a cylinder look like?

• The net of a cylinder consists of two circles and a rectangle

• The length of the rectangle is equal to the circumference of the circles

  • $\mathrm{Circumference}=2\timesπ\times\mathrm{radius}$

• The width of the rectangle is equal to the height of the cylinder

Net of a cylinder

What does the net of a pyramid look like?

• The net of a square-based pyramid consists of one square and four congruent (identical) triangles

  • The perpendicular height of each triangle is equal to the slant height of the pyramid

Example of a net of a pyramid

Exam Hint You may be given the dimensions of the solid when asked to draw a net.

Make sure you put the correct lengths in the correct places by imagining cutting out and folding up the net.

Worked Example A cuboid measures 6 cm by 3 cm by 2 cm.

On the 1 cm² grid, draw an accurate net of this cuboid. One face has been drawn for you.

Answer:

The cuboid has three pairs of rectangles; measuring 6 cm by 3 cm, 6 cm by 2 cm, and 3 cm by 2 cm

Make sure the net has two of each of these rectangles in the correct places