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Problem 257

Geometry Difficulty 1.4 Multiple choice CEMC Cayley · Canada · 2022

Two identical smaller cubes are stacked next to a larger cube.
Each of the two smaller cubes has a volume of 8. The combined height of
the smaller cubes equals the height of the larger cube. What is the
volume of the larger cube?

Pick one

Official solution

Since $2 \times 2 \times 2 = 8$ , a cube with edge length 2 has volume 8. (We note also that
$\sqrt[3]{8} = 2$ .)

Therefore, each of the cubes with volume 8 have a height of 2.

This means that the larger cube has a height of $2+2 = 4$ , which means that its volume is
$4^3 = 4 \times 4 \times 4 = 64$ .

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.