Question

question find the volume of a pyramid with a square base, where the side length of the base is 14.1 ft and the height of the pyramid is 13.1 ft. round your answer to the nearest tenth of a cubic foot. answer attempt 1 out of 2 ft³

Explanation:

Step1: Recall volume formula for square - based pyramid

The volume formula for a square - based pyramid is $V=\frac{1}{3}Bh$, where $B$ is the area of the base and $h$ is the height. Since the base is a square, if the side length of the base is $s$, then $B = s^{2}$.

Step2: First, find the area of the base

Given the side length of the base $s = 14.1$ ft, then $B=s^{2}=(14.1)^{2}=198.81$ square - feet.

Step3: Then, find the volume

The height $h = 13.1$ ft. Using the volume formula $V=\frac{1}{3}Bh$, substitute $B = 198.81$ and $h = 13.1$ into it. So $V=\frac{1}{3}\times198.81\times13.1=\frac{1}{3}\times2604.411 = 868.137$ cubic - feet.

Step4: Round to the nearest tenth

Rounding $868.137$ to the nearest tenth gives $868.1$ cubic - feet.

Answer:

$868.1$