All corners were sliced off of a cube whose volume was 2000 cubic centimeters.

Question

Triangular faces are not located where the cube's vertices were. Each triangle is equilateral with 5-centimeter sides. Determine the number of edges on the new solid.

Answer 1

The question asks how many edges are on the new solid when each vertex of a cube are replaced by a triangular face. So there are some questions that need to be asked first. How many vertexes does the original cube contain? How long are the sides of the cube before the vertices are removed? Are the edges of the cube still present after the vertices are removed (as in, do the equilateral triangles meet along the original edges or not)

If you draw a picture of a cube, it is easy to see that there are 8 vertices on the cube, 4 on the top where the face and two sides intersect and 4 on the bottom. When each vertex is replace by an equilateral triangle faces, three new edges are formed. Therefore there are 8*3 = 24 edges due to the equilateral triangle faces replacing the vertices of the cube.

The question that remains is do the triangles eliminate the edges between the faces on the cube?

The cube has a volume of 2000 cm^3, the volume of a cube is V = s^3 where s is the length of a side. The length of the side of the cube is therefore s = V^(1/3) = (2000 cm^3)^(1/3) = 12.6 cm

Since the sides of the equilateral triangles formed when the vertices of the cube are removed are 5 cm on the side, they extend less than 5 cm along an edge of the cube (we could figure out exactly how far, but that doesn't really matter), so all the original edges of the cube still remain.

The original cube has 4 edges where sides intersect the top, 4 edges where sides intersect sides, and 4 edges where the sides intersect the bottom, for a total of 12 sides.

Adding up the new and existing edges: 24 + 12 = 36 edges

Answer 2

Sketch a diagram!

In addition to the original 12 edges, the triangles create 24 more (8 x 3).