Question

an artist is building a rectangular pyramid - shaped installation for an art festival. the base of the pyramid measures 11 meters by 7 meters, and the height from the apex to the center of the base is 16 meters. to complete the installation, the artist needs to determine the total volume of the structure to estimate the materials needed.
how much space will the installation 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 rectangle. The area formula for a rectangle is \(A = l\times w\), where \(l = 11\) meters and \(w = 7\) meters.
\(A=11\times7 = 77\) square meters.

Step2: Use the volume formula for a pyramid

The volume formula for a pyramid is \(V=\frac{1}{3}Ah\), where \(A\) is the base area and \(h\) is the height. Here, \(A = 77\) square meters and \(h = 16\) meters.
\(V=\frac{1}{3}\times77\times16=\frac{1232}{3}\approx411\) cubic meters.

Answer:

411