Problem 15 · 2009 Math Kangaroo
Medium
Geometry & Measurement
factorizationspatial-reasoning
We want to build a box with measurements 40 × 40 × 60 using identical cubes. What is the smallest number of cubes needed?
Show answer
Answer: B — 12
Show hints
Hint 1 of 2
Using as few cubes as possible means using the largest cube that fits all three dimensions.
Still stuck? Show hint 2 →
Hint 2 of 2
The cube edge must divide 40, 40 and 60 — take their greatest common factor.
Show solution
Approach: largest common cube
- The cube edge must divide 40, 40 and 60; the greatest such length is 20.
- The box holds (40÷20) × (40÷20) × (60÷20) = 2 × 2 × 3 cubes.
- That is 12 cubes — answer B.
Mark:
· log in to save