He measured the height of the box to be 3 in. Then, Stephan drew a line from the center of one of the hexagons to each of its vertices and noticed that all the triangles he created have a height of 5 in and a base of 6 in.

Answer 1

Based on this information, we can assume that each side of the hexagon is also 6 inches long (since the base of each triangle is one side of the hexagon).

To find the area of one hexagon, we can use the formula:

Area = (3√3)/2 x s^2

where s = length of one side of the hexagon.

Plugging in s = 6, we get:

Area = (3√3)/2 x 6^2
Area = (3√3)/2 x 36
Area = 54√3

So the area of one hexagon is 54√3 square inches.

To find the volume of the box, we multiply the area of one hexagon by the height of the box:

Volume = 54√3 x 3
Volume = 162√3 cubic inches.

Therefore, the volume of the box is 162√3 cubic inches.