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 base a regular hexagon, height h = 6 ft, side length s = 6 ft
options: 216 ft³, 187 ft³, 31 ft³, 561 ft³

Explanation:

Step1: Recall pyramid volume formula

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

Step2: Identify given values

We know that the area of the base \( B = 93.5 \, \text{ft}^2 \) and the height \( h = 6 \, \text{ft} \).

Step3: Substitute values into formula

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

Answer:

\( 187 \, \text{ft}^3 \) (corresponding to the option "187 ft³")