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 pyramid with h = 6 ft, s = 6 ft options: 187 ft³, 561 ft³, 216 ft³, 31 ft³

Explanation:

Step1: Recall the volume formula for a pyramid

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

Step2: Identify the values of \( B \) and \( h \)

From the problem, the area of the base (regular hexagon) \( B = 93.5\space\text{ft}^2 \) and the height of the pyramid \( h = 6\space\text{ft} \).

Step3: Substitute the values into the formula

Substitute \( B = 93.5 \) and \( h = 6 \) into the volume formula:
\( V=\frac{1}{3}\times93.5\times6 \)
First, calculate \( 93.5\times6 = 561 \), then divide by 3: \( \frac{561}{3}=187 \).

Answer:

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