Question

a water reservoir is shaped like a square pyramid. the base area of the pyramid is 72.4 square meters, and the height from the center of the base to the vertex is 12 meters. how much water can the reservoir hold when filled to the top? round your answer to the nearest tenth if necessary. use the keypad to type your answer in the box provided. the amount of water the reservoir can hold is cubic meters.

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

Given \( B = 72.4\) square meters and \( h=12\) meters.
Substitute into \( V=\frac{1}{3}\times72.4\times12\).
First, calculate \( 72.4\times12 = 868.8\).
Then, \( V=\frac{1}{3}\times868.8\).

Step3: Calculate the volume

\( V=\frac{868.8}{3}=289.6\)

Answer:

\(289.6\)