Problem 8 · 2022 Math Kangaroo
Medium
Spatial & Visual Reasoning
cube-views
Sonja builds the cube shown out of equally sized bricks. The shortest edge of one brick is 4 cm long. What are the dimensions, in cm, of one brick?
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Answer: C — \(4 \times 8 \times 12\)
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Hint 1 of 2
The shortest brick side is 4 cm; use the cube picture to count how many bricks line up along each edge.
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Hint 2 of 2
Each brick edge must fit a whole number of times along the cube's edge, so all three brick lengths divide the cube's side.
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Approach: read the brick counts off the cube picture
- The cube is built from equal bricks whose shortest side is 4 cm, so the cube's edge is a multiple of 4.
- Counting the bricks along the three directions in the figure shows the brick is 4 cm by 8 cm by 12 cm, and 24 (the cube edge) is divisible by each of these.
- So one brick measures 4 x 8 x 12 cm, the answer is C.
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