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Problem 251

Geometry Difficulty 2.1 Find the answer CEMC Cayley

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

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

Since $2 \times 2 \times 2=8$ , a cube with edge length 2 has volume 8. 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: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.