Question

a monument is shaped like a square pyramid with a total volume of 2,400 cubic meters. the height of the pyramid, measured from the center of the base to the vertex, is 20 meters. what is the side length of the base of the monument? round your answer to the nearest whole number. use the keypad to type your answer in the box provided. the side length of the base of the monument is meters.

Explanation:

Step1: Recall the volume formula for a square - pyramid

The volume formula for a square - pyramid is \(V=\frac{1}{3}s^{2}h\), where \(V\) is the volume, \(s\) is the side length of the base, and \(h\) is the height.
We are given that \(V = 2400\) cubic meters and \(h=20\) meters.

Step2: Substitute the given values into the formula

Substitute \(V = 2400\) and \(h = 20\) into \(V=\frac{1}{3}s^{2}h\).
We get \(2400=\frac{1}{3}s^{2}\times20\).
First, simplify the right - hand side: \(\frac{1}{3}\times20=\frac{20}{3}\). So the equation becomes \(2400=\frac{20}{3}s^{2}\).

Step3: Solve for \(s^{2}\)

Multiply both sides of the equation by \(\frac{3}{20}\) to isolate \(s^{2}\).
\(s^{2}=2400\times\frac{3}{20}\).
\(2400\div20 = 120\), and \(120\times3=360\). So \(s^{2}=360\).

Step4: Solve for \(s\)

Take the square root of both sides: \(s=\sqrt{360}\).
\(\sqrt{360}=\sqrt{36\times10}=6\sqrt{10}\approx6\times3.162 = 18.972\).
Rounding \(18.972\) to the nearest whole number gives \(s\approx19\).

Answer:

19