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.
(diagram of a pyramid with h = 6 ft and s = 6 ft)
options: 187 ft³, 561 ft³, 31 ft³, 216 ft³

Explanation:

Step1: Recall the volume formula for a 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: Substitute the given values into the formula

We are given that \( B = 93.5\space ft^{2}\) and \( h=6\space ft\). Substitute these values into the formula: \( V=\frac{1}{3}\times93.5\times6\).
First, calculate \(93.5\times6 = 561\). Then, \(V=\frac{561}{3}\).

Step3: Simplify the expression

\(V = 187\space ft^{3}\).

Answer:

\(187\space ft^{3}\)