Problem 13 · 2020 Math Kangaroo
Stretch
Spatial & Visual Reasoning
cube-viewsarea
Zilda will use six identical cubes and two different rectangular blocks to build the structure shown, which has eight faces. Before gluing the pieces, she paints each one completely and works out that she needs 18 litres of paint (colour does not matter). How many litres of paint would she use if she painted the whole structure only after gluing the pieces together?
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Answer: C — 11.5
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Hint 1 of 2
Painting after gluing simply skips the faces that get hidden where two pieces touch.
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Hint 2 of 2
Every internal contact hides two equal faces, so pair them up and remove their paint.
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Approach: subtract the paint on the faces hidden by gluing
- Painted separately, all the pieces' faces need 18 litres.
- After gluing, wherever two pieces meet, two equal faces are hidden and no longer painted, so that paint is removed.
- Totalling the hidden contact faces and subtracting their paint from 18 litres leaves 11.5 litres, option C.
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