Problem 21 · 2011 Math Kangaroo
Stretch
Geometry & Measurement
area-fractionsymmetry
Simon has a glass cube with side length 1 dm. He sticks several equally big black squares on it, as shown, so that all faces look the same. How many cm² were covered over?
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Answer: C — 225
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Hint 1 of 2
The cube has edge 10 cm, so its total surface area is 6 × 10².
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Hint 2 of 2
Find what fraction of each identical face the black squares cover, then take that share of the surface.
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Approach: take the covered fraction of the total surface
- A 1 dm cube has edge 10 cm, so its surface area is 6 × 10² = 600 cm².
- The pattern is identical on every face, so the same fraction of each 100 cm² face is black.
- That fraction works out to ⅜ of each face, and ⅜ of 600 = 225 cm².
- So 225 cm² were covered, choice (C).
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