15.5 Accurate Drawings 2

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: nets of 3D solids, folding nets, and drawing prisms and pyramids. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

• Recognise and draw nets of cubes, cuboids, prisms and pyramids
• Work out which faces, edges and corners meet when a net is folded
• Use a net to find the total area of the faces of a solid
• Draw prisms and pyramids using their end faces on squared or isometric paper

Key words

• Net: A flat 2D shape that folds up to make a 3D solid.
• Opposite faces: Faces of a cuboid that do not touch, such as the top and the bottom.
• Surface area: The total area of all the faces of a solid. It equals the area of its net.
• Oblique drawing: A drawing with the front face drawn true shape and the depth drawn at an angle.

Nets of a cube

A cube has 6 square faces, so every net of a cube has 6 squares. There are exactly 11 different nets of a cube. Not every arrangement of 6 squares works: some faces end up on top of each other.

Worked example: testing a net

Is a 2 by 3 rectangle of squares a net of a cube?
Fold the top row up: the three squares make a "U" with the bottom row. The two middle squares both become the same face.

Answer: No. Two squares overlap and one face is missing.

Nets of other solids

A prism net has the two end faces plus one rectangle for each side of the end. A pyramid net has the base plus one triangle for each side of the base.

Worked example: net of a cuboid and its area

Sketch a net of a 4 cm by 3 cm by 2 cm cuboid and find its total area.
The net has two of each rectangle: 4 × 3, 4 × 2 and 3 × 2.
Area = 2 × 12 + 2 × 8 + 2 × 6 = 24 + 16 + 12 = 52 cm²

Answer: 52 cm² (this is the surface area of the cuboid)

Folding a net

Choose one face as the base. Imagine folding the others up around it. Faces with exactly one square between them in a straight line are opposite each other.

Worked example: opposite faces

In the net above, B is the base. L and R are either side of B in a row, so they are opposite.
F and K are either side of B in the column, so they are opposite. T is joined to K and folds over the top.

Answer: L opposite R, F opposite K, B opposite T

Key fact: On a normal dice the numbers on opposite faces add up to 7: 1 and 6, 2 and 5, 3 and 4.

Drawing prisms and pyramids

To draw a prism, draw the end face first. Copy it a little up and to the right, then join matching corners. To draw a pyramid, draw the base as a parallelogram, mark the apex above the centre and join it to each corner. Hidden edges are dashed.

Worked example: the L-shaped prism

The end face is an L shape 3 squares wide and 3 squares tall.
The back face is drawn 2 squares right and 1 square up. Matching corners are joined with parallel lines.

Answer: an L-shaped prism with 8 faces

Common mistakes

• Thinking any 6 squares joined together make a cube net. Always imagine folding it.
• Drawing a prism net with the end faces on the wrong rectangles, so they do not close the ends.
• Missing faces when finding the area of a net: a cuboid has 3 pairs of equal faces.
• Drawing the back face of a prism a different size or shape from the front face.

Revision questions

Try these, then check your answers below each one.

Question 1. How many faces does the net of a triangular prism have? (Choose from: 5, 6, 4, 9.)

Answer: 5

Working: 2 triangles and 3 rectangles: 5 faces.

Question 2. True or false? A 2 by 3 rectangle made of six squares is a net of a cube.

Answer: False

Working: When folded, two squares end up on the same face, and one face is missing. False.

Question 3. Work out the total area of the net of a cuboid 6 cm by 4 cm by 3 cm.

Answer: 108 cm²

Working: 2 × (6 × 4 + 6 × 3 + 4 × 3) = 2 × 54 = 108 cm².

Related lessons

• Previous lesson: 15.4 Scale Drawings and Maps
• Next lesson: 15.6 Constructions
• In this chapter: 15.1 3D Solids
• In this chapter: 15.2 Plans and Elevations
• In this chapter: 15.3 Accurate Drawings 1

Continue in the full course

This lesson is section 15.5 (EGCMF1505) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.