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A hexagonal pyramid is 14 meters tall, and the length of a side is 7 meters. Calculate its volume if its apothem is 3.5 meters.

A) 176√3 m³
B) 294 m³
C) 147 m³
D) 420 m³

1 Answer

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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.

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