Maths Olympiad Prep

Track / Stage 1 / 287 of 320 #287 of 2604

Problem 287

Geometry Difficulty 1.6 Multiple choice CEMC Gauss (Grade 7) · Canada · 2015

One corner of a cube is cut off, creating a new triangular face, as shown.

Figure 0

How many edges does this new solid have?

Pick one

Next problem →

Official solution

The original cube (before the corner was cut off) had 12 edges.

Cutting off the corner does not eliminate any of the 12 edges of the original cube.
However, cutting off the corner does add 3 edges that were not present originally, the 3 edges of the new triangular face. Since no edges of the original cube were lost, but 3 new edges were created, then the new solid has 12+3=1512+3=15 edges.

Figure for this problem

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