Problem 8 · 2025 AMC 8
Medium
Geometry & Measurement
spatial-reasoningareasquare-area
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Answer: A — 3√3 cubic centimeters.
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Hint 1 of 2
Unfolding doesn't change the cardboard. A cube has 6 identical square faces — what's the area of just one of them?
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Hint 2 of 2
One face has area 18 ÷ 6 = 3. From a square's area you can get its side, and from the side you can get the volume.
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Approach: area → side → volume
- The flat shape is the cube's 6 faces, all identical squares, so one face has area 18 ÷ 6 = 3. That gives the side directly: side = √3.
- Volume = side3 = (√3)3 = (√3)2 × √3 = 3√3, so 3√3.
- Why this transfers: the chain area → length → volume is one you'll reuse constantly — a square's side is √(area), and a cube's volume is that side cubed. Don't be thrown by the answer being a surd; (√3)3 = 3√3, not a whole number.
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