Question

the base of the pyramid in the diagram is a regular hexagon. the length of each side of the hexagon is 6 ft and the height of the pyramid is 6 ft. the area of the regular hexagon is 93.5 ft². what is the volume of the pyramid? round your answer to the nearest cubic foot.

Explanation:

Step1: Recall pyramid volume formula

The volume $V$ of a pyramid is given by $V = \frac{1}{3} \times B \times h$, where $B$ is the base area and $h$ is the height of the pyramid.

Step2: Substitute given values

We know $B = 93.5 \text{ ft}^2$ and $h = 6 \text{ ft}$. Substitute these into the formula:
$V = \frac{1}{3} \times 93.5 \times 6$

Step3: Calculate the volume

First compute $93.5 \times 6 = 561$, then multiply by $\frac{1}{3}$:
$V = \frac{561}{3} = 187$

Answer:

187 cubic feet