Problem 14 · 2015 Math Kangaroo
Medium
Geometry & Measurement
area
A cuboid shaped container has a square base with side length 10 cm. It is filled up to a height h with water. Now a metal cube with side length 2 cm is put inside. It sinks to the bottom of the container. The water now reaches to the top corner of the metal cube. Determine h!
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Answer: A — 1.92 cm
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Hint 1 of 2
The cube sinks fully; the water surface ends level with the cube's top, i.e. at height 2 cm.
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Hint 2 of 2
Volume of water is fixed: it equals the 10×10×2 block minus the 2×2×2 cube.
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Approach: conserve the water volume
- The water rises to the cube's top, so the final level is 2 cm.
- Up to height 2, the container holds 10 × 10 × 2 = 200 cm³, but the cube occupies 2³ = 8 cm³.
- Water volume = 200 − 8 = 192 cm³, and originally that filled 10 × 10 × h = 100h.
- So h = 192 / 100 = 1.92 cm.
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