Problem 27 · 2018 Math Kangaroo
Stretch
Spatial & Visual Reasoning
cube-viewsshadows-projections
Seven little dice were removed from a 3 × 3 × 3 die, as shown in the diagram. The remaining (completely symmetrical) figure is cut along a plane through the centre and perpendicular to one of the four space diagonals. What does the cross-section look like?
Show answer
Answer: A
Show hints
Hint 1 of 2
Looking straight down a space diagonal of a cube, the outline you see is a regular hexagon.
Still stuck? Show hint 2 →
Hint 2 of 2
Track which little cubes were removed and where their gaps fall on that hexagonal cross-section.
Show solution
Approach: take the cross-section perpendicular to a space diagonal
- Viewed along a space diagonal, the cube's cross-section through the centre is a regular hexagon.
- Removing the seven little cubes (the centre and the six face-centres) leaves gaps that, on this cross-section, form a six-pointed star.
- So the cross-section looks like option A (the star inside the hexagon).
Mark:
· log in to save