Final answer:
To calculate the volume of a hexagonal pyramid, you need to know the height, length of a side, and apothem. The formula for the volume of a pyramid is given by V = (1/3) * base_area * height. Given the height (h = 14 m), side length (s = 7 m), and apothem (a = 3.5 m), the volume of the hexagonal pyramid is 294 m³.
Step-by-step explanation:
A hexagonal pyramid consists of a hexagonal base and triangular faces that meet at a common vertex.
To calculate the volume of a hexagonal pyramid, you need to know the height, length of a side, and apothem. The formula for the volume of a pyramid is given by:
V = (1/3) * base_area * height
For a hexagonal pyramid, the base_area is given by:
base_area = (3 * √3 * side_length^2) / 2
Given the height (h = 14 m), side length (s = 7 m), and apothem (a = 3.5 m), we can substitute these values into the formula to find the volume:
V = (1/3) * ((3 * √3 * 7^2) / 2) * 14 = 294 m³
Therefore, the volume of the hexagonal pyramid is 294 m³.