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Primary 6 · Volume · Question type 7.3

P6 Volume: Counting Cubes from Front, Side and Top Views

Count every unit cube by comparing the front, side and top views, including hidden cubes.

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Primary 6, on the MOE Primary Mathematics syllabus.

In the Volume chapter7 question types · see the chapter

The lesson · 2 minutes 7 seconds

How do you count cubes from front, side and top views in P6?

Watch: a solid of unit cubes, seen from the front, the side and the top

Another worked example

A worked example

A block is built from 1-cm cubes, 6 cubes long, 5 cubes deep and 4 cubes high. Every face of the block is painted, including the base. The block is then taken apart into its 1-cm cubes, and the cubes are sorted into groups by the number of faces that are painted. How many cubes are in the largest group?

The working · Nine lines

The step-by-step working

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

  1. inner length = 6 - 2 = 4
  2. inner depth = 5 - 2 = 3
  3. inner height = 4 - 2 = 2
  4. cubes with 3 faces painted = 8
  5. cubes with 2 faces painted = (4 + 3 + 2) × 4 = 36
  6. cubes with 1 face painted = (4 × 3 + 4 × 2 + 3 × 2) × 2 = 52
  7. cubes with 0 faces painted = 4 × 3 × 2 = 24
  8. total = 8 + 36 + 52 + 24 = 120
  9. largest group = 52 cubes

The answer is 52 cubes.

Practise · Modelled on top school exam questions

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Count cubes from views

Use the views to find how many hidden cubes can be added.

Unit cubes are stacked in a corner inside a box 4 cubes long, 4 cubes deep and 3 cubes high. Counting rows from the front, the front two rows are completely filled to the full height of 3. In each of the back two rows, only the cubes at the two ends are there, stacked to the full height of 3. What is the GREATEST number of unit cubes that can be added without changing the front view or the side view?

Show the step-by-step solution
  1. hidden columns = 2 × 2 = 4
  2. each column fills to the top = 4 × 3 = 12

Ans: 12

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Next, convert between litres, millilitres and cubic centimetres. Litres, Millilitres and Cubic Centimetres →

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