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: 216 ft³, 31 ft³, 561 ft³, 187 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) \( B = 93.5 \, \text{ft}^2 \) and the height \( h = 6 \, \text{ft} \).

Step3: Substitute the values into the formula

Substitute \( B = 93.5 \) and \( h = 6 \) into the formula \( V = \frac{1}{3}Bh \):
\[
V = \frac{1}{3} \times 93.5 \times 6
\]
First, calculate \( 93.5 \times 6 = 561 \), then divide by 3: \( \frac{561}{3} = 187 \).

Answer:

\( 187 \, \text{ft}^3 \) (the option: \( 187 \, \text{ft}^3 \))