Find the volume of a regular hexagonal prism with each edge equal to 8.

The volume of the prism is found by the formula:
V = S * H,
where S is the area of ​​the base of the prism, H is the height of the prism.
Since each edge of a regular hexagonal prism is 8, at its base lies a regular hexagon, each side of which is 8. The area of ​​a regular hexagon is found by the formula:
S = (3√3 * a²) / 2,
where a is the length of the side of the hexagon.
By condition, a = 8, then:
S = (3√3 * 8²) / 2 = (3√3 * 64) / 2 = 3√3 * 32 = 96√3.
Since the height of a regular hexagonal prism is equal to the length of its edge, then H = 8.
Let’s find the volume of the prism given by the condition:
V = S * H ​​= 96√3 * 8 = 768√3.
Answer: V = 768√3.