Math Snap

STEP 1

1. The base of the pyramid is a regular hexagon.
2. Each side of the hexagon measures $6$ feet.
3. The height of the pyramid is $6$ feet.
4. The area of the hexagonal base is $93.5$ square feet.

STEP 2

1. Recall the formula for the volume of a pyramid.
2. Substitute the given values.
3. Calculate the volume.
4. Round the volume to the nearest cubic foot.

STEP 3

Recall the formula for the volume of a pyramid:
$$V = \frac{1}{3} \times \text{Base Area} \times \text{Height}$$

STEP 4

Substitute the given values into the formula:
$$V = \frac{1}{3} \times \text{Base Area} \times \text{Height}$$ $$= \frac{1}{3} \times 93.5 \text{ft}^2 \times 6 \text{ft}$$

STEP 5

Calculate the product:
$$V = \frac{1}{3} \times 93.5 \text{ft}^2 \times 6 \text{ft}$$ $$= \frac{1}{3} \times 561 \text{ft}^3$$ $$= 187 \text{ft}^3$$

Round the volume to the nearest cubic foot:
The volume is already a whole number, so no rounding is necessary.
The volume of the pyramid is:
$$\boxed{187 \text{ft}^3}$$