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Question P6 Seeing it move

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Painted block — Ravi cuts it into cubes

Ravi had a rectangular block of wood 10 cm by 5 cm by 4 cm. He painted all the faces of the block.

  1. (a) What is the total painted area?
  2. (b) Ravi cut the block into 1-cm cubes. How many of these cubes have (i) none of the faces painted? (ii) 2 of the faces painted?

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About this method

Seeing it move

Work out where the pieces land after a fold, cut or stack.

In this one. A small cube is painted on exactly the block faces it touches — so "0 faces" means strip a 1-cm skin off all six sides and count what is left, and "2 faces" means it lies on an edge but is not a corner.

ABCDEFa straight strip of three: the two ends land opposite

How to spot it

Words like 'folded', 'cut along the dotted line' or 'stacked' appear beside a shape, and the question asks for a length or angle that only makes sense once the pieces are in their new positions.

Common mistake

Children try to calculate the answer before working out where the pieces actually end up, skipping the visualisation step that the whole question depends on.

Practise a similar question

Challenging Ravi has a square piece of canvas of side 31 cm. He cuts along the dotted lines to get one small square of area 289 cm² and 8 identical right-angled triangles. Triangle XYZ is one such triangle. Find the length of XY.
All 8 with this pattern →
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