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 volume formula for pyramid

The volume formula for a pyramid is $V=\frac{1}{3}Bh$, where $B$ is the base - area and $h$ is the height.

Step2: Identify base - area and height values

We are given that the base - area $B = 93.5$ ft² and the height $h=6$ ft.

Step3: Calculate the volume

Substitute the values into the formula: $V=\frac{1}{3}\times93.5\times6$. First, calculate $\frac{1}{3}\times6 = 2$. Then, $V=2\times93.5=187$ ft³.

Answer:

$187$ ft³