Question

Your class tried to construct a tetrahedron using four smaller congruent tetrahedra. However, the result left a gap in the center, as shown in the diagram below. If the volume of each small shaded tetrahedron is 50 in.3, what is the volume of the gap? Explain how you know.

Answer 1

200 in³

Step-by-step explanation:

The lengths of the sides of the constructed tetrahedron are twice the length of the side of the small tetrahedron of 50 in³. It means that the scale factor for the solid is 2. So, the complete volume of the constructed tetrahedron is equal to

Vn = 2³(50 in³)

Vn = 8(50 in³)

Vn = 400 in³

However, we only use 4 small tetrahedrons, so the volume of these four solids is

4(50 in³) = 200 in³

Then, the volume of the gap is the difference between the volume of the constructed tetrahedron and the volume of the 4 small tetrahedrons

400 in³ - 200 in³ = 200 in³

So, the answer is 200 in³