Problem 23 · 2022 Math Kangaroo
Stretch
Spatial & Visual Reasoning
cube-viewscareful-counting
The big cube is built from three different kinds of building blocks (see diagram). How many of the little white cubes are needed to build the big cube?
Show answer
Answer: B — 11
Show hints
Hint 1 of 3
First figure out how many little cubes fill the whole big cube — it is 3 across, 3 deep and 3 tall.
Still stuck? Show hint 2 →
Hint 2 of 3
Each grey L-piece and each dark bar is made of 3 little cubes, so count how many little cubes all the coloured pieces use up.
Still stuck? Show hint 3 →
Hint 3 of 3
Whatever little cubes are left over after the coloured pieces must be the single white ones.
Show solution
Approach: count all the little cubes, then take away the coloured pieces
- The big cube is 3 across, 3 deep and 3 tall, so it holds 3 × 3 × 3 = 27 little cubes.
- Each grey L-piece and each dark bar is built from 3 little cubes, and together the coloured pieces fill 16 of the 27 spots.
- Every spot that is left over must be a single white cube: 27 − 16 = 11.
- So 11 little white cubes are needed (choice B).
Mark:
· log in to save