Problem 20 · 2020 Math Kangaroo
Stretch
Geometry & Measurement
areaspatial-reasoning
Two rectangular blocks and a cube are joined to form a larger rectangular block of volume 280 cm³. The cube, shown in dark gray, has volume 125 cm³, and the smaller rectangular block has volume 75 cm³. What is the area of the face marked with the question mark?
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Answer: A — 16 cm²
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Hint 1 of 2
The cube has side 5, so one dimension of everything is 5.
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Hint 2 of 2
Slice the big block into a 5-thick slab and split its face into the three pieces.
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Approach: decompose the 5x7x8 block
- The total volume 280 = 5×7×8, and the cube (125) is 5×5×5.
- Removing the cube's 5×5 corner from the 7×8 face leaves an L of area 31, split as 15 (the 75-block, 5×5×3) and 16 (the 80-block, 5×4×4).
- The marked face is that 4×4 face = 16 cm².
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