Question

no additional details were added for this assignment.
given by $v = \frac{1}{3}bh$
where $v$ is the volume of the pyramid, $b$ is the area of the base, and $h$ is the height of the pyramid.
a monument in the shape of a square pyramid is being constructed to honor local heroes. the side length of the square base is 9 meters, and the height from the apex of the pyramid to the center of the base is 21 meters.
how much space will the pyramid occupy? round your answer to the nearest whole number.
use the keypad to enter the answer in the box.
the volume of the installation is □ cubic meters.

Explanation:

Step1: Calculate the area of the base

The base is a square with side length \(a = 9\) meters. The area of a square is \(B=a^{2}\). So, \(B = 9\times9=81\) square meters.

Step2: Substitute into the volume formula

The volume formula for a pyramid is \(V=\frac{1}{3}Bh\). We know \(B = 81\) and \(h = 21\). Substitute these values: \(V=\frac{1}{3}\times81\times21\).
First, \(\frac{1}{3}\times81=27\). Then, \(27\times21 = 567\).

Answer:

\(567\)