## 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: $36$