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Primary 6 · Solids · Question type 10.3

P6 Solids: Exposed Faces of Joined Cubes

Start with 6 faces for each cube, then subtract one for every glued face and one for a face resting on the table.

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Primary 6, on the MOE Primary Mathematics syllabus.

In the Solids chapter4 question types · see the chapter

The lesson · 2 minutes 20 seconds

How do you count exposed faces of joined cubes in P6?

Watch: 7 unit cubes glued into one solid, and which of them the brush reaches on exactly 4 faces

Another worked example

A worked example

Ten unit cubes are glued together to form the staircase shown, one cube deep, with columns 4, 3, 2 and 1 cubes high. The outside is painted, but the faces resting on the table are not painted. How many faces of the cubes are painted altogether?

The working · Six lines

The step-by-step working

Written out in full, the way it should appear on paper.

  1. faces on 10 loose cubes = 10 x 6 = 60
  2. joins up the four columns = 3 + 2 + 1 = 6
  3. joins between neighbouring columns = 3 + 2 + 1 = 6
  4. faces hidden by joins = 12 x 2 = 24
  5. cubes standing on the table = 4
  6. painted faces = 60 - 24 - 4 = 32

The answer is 32.

Practise · Modelled on top school exam questions

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Total painted faces

Start with the outside faces and account for shared joins.

Seven unit cubes are glued together to form the solid shown. The whole outside of the solid is then painted, including the faces that rest on the table. How many faces of the cubes are painted altogether?

Show the step-by-step solution
  1. faces on 7 loose cubes = 7 x 6 = 42
  2. the cubes are glued at 6 joins, and each join hides 2 faces = 6 x 2 = 12
  3. painted faces = 42 - 12 = 30

Ans: 30

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