Question

The hexagonal prism and hexagonal pyramid have the same base and the same height. The volume of the hexagonal prism is 66 cubic units. What is the volume of the pyramid?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the volume of the pyramid, we first need to find the area of the base.

The area of a regular hexagon can be calculated using the formula:
Area = (3√3/2) * s^2

Where s is the side length of the hexagon. Since the pyramid and prism have the same base, the area of the base of the prism is the same as the area of the base of the pyramid.

Now, we know that the volume of the prism is 66 cubic units. The volume of a prism can be calculated using the formula:
Volume = Base Area * Height

Given that the heights of the prism and the pyramid are the same, the volume of the pyramid can be calculated as follows:
Volume = 66 / 3 = 22 cubic units

Therefore, the volume of the hexagonal pyramid is 22 cubic units.