Problem 3 · 2010 Math Kangaroo
Medium
Geometry & Measurement
areaspatial-reasoning
The hollow spaces of two empty containers are cubic and have a base area of 1 dm² and 4 dm² respectively. The big container is to be filled with water, using the small one as a scoop. How many full scoops are necessary to fill the big cube?
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Answer: D — 8
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Hint 1 of 2
Both hollows are cubes, so a base area also fixes the height.
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Hint 2 of 2
Compare the two volumes, not the base areas.
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Approach: turn base areas into side lengths, then volumes
- A cube with base 1 dm² has side 1 dm, so volume 1 dm³.
- A cube with base 4 dm² has side 2 dm, so volume 2³ = 8 dm³.
- Filling 8 dm³ one scoop (1 dm³) at a time needs 8 scoops.
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