Corners of a Cube

All corners were sliced off a cube whose volume was 2000 cubic centimeters. Triangular faces are located where the cube’s vertices were. Each triangle is equilateral with 5-centimeter sides. Determine the total numbers of edges on the new solid.
Source: NCTM Mathematics Teacher, January 2006

Solution
A cube has 12 edges and 8 vertices. If each vertex is sliced off and replaced by a triangle, 8\times 3=24 more edges are added on the new solid. Thus, the total number of edges equals 12+24=36.

Answer: 36

 

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About mvtrinh

Retired high school math teacher.
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