Question

a sculpture exhibit features a decorative pyramid made of translucent material. the pyramid has a square base with a side length of 3.7 meters. the height of the pyramid from the center of the base to the vertex is 8.4 meters. what is the total volume of the pyramid? round your answer to the nearest tenth. use the keypad to type your answer in the box provided. the total volume of the pyramid is □ cubic meters.

Explanation:

Step1: Calculate the base area

The base is a square with side length \(a = 3.7\) meters. The area of a square is \(A=a^{2}\). So, \(A=(3.7)^{2}=13.69\) 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, \(A = 13.69\) and \(h=8.4\). Then \(V=\frac{1}{3}\times13.69\times8.4\).
First, calculate \(13.69\times8.4 = 115.0\) (approximate \(13.69\times8.4=(13 + 0.69)\times8.4=13\times8.4+0.69\times8.4 = 109.2+5.796 = 114.996\)).
Then \(V=\frac{1}{3}\times114.996 = 38.332\).

Answer:

\(38.3\)