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Problem 302

Geometry Difficulty 2.2 Multiple choice CEMC Cayley · Canada · 2023

The surface area of a cube is 24. The volume of the cube is

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Official solution

A cube has six identical faces.

If the surface area of a cube is 24, the area of each face is 246=4\frac{24}{6} = 4.

Since each face of this cube is a square with area 4, the edge length of
the cube is 4=2\sqrt{4} = 2.

Thus, the volume of the cube is 232^3
which equals 8.

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