Question

the image shows a reconstruction of a pyramid with a square base. what is the best estimate for the volume of the pyramid?
a. 1,460,040 m³
b. 2,433,400 m³
c. 4,380,120 m³
d. 7,300,200 m³

Explanation:

Step1: Recall the volume formula for a square - based pyramid

The volume \(V\) of a pyramid with a square base is given by the formula \(V=\frac{1}{3}Bh\), where \(B\) is the area of the base and \(h\) is the height of the pyramid. For a square base with side length \(s\), the area of the base \(B = s^{2}\).
Here, the side length of the square base \(s = 230\) meters and the height \(h=138\) meters.

Step2: Calculate the area of the base

First, we calculate the area of the square base. Using the formula \(B = s^{2}\), substituting \(s = 230\) meters, we get \(B=(230)^{2}=230\times230 = 52900\space m^{2}\).

Step3: Calculate the volume of the pyramid

Now, we use the volume formula for the pyramid \(V=\frac{1}{3}Bh\). Substitute \(B = 52900\space m^{2}\) and \(h = 138\) meters into the formula:
\(V=\frac{1}{3}\times52900\times138\)
First, calculate \(52900\times138 = 52900\times(140 - 2)=52900\times140-52900\times2=7406000 - 105800=7299200\)
Then, \(\frac{1}{3}\times7299200\approx\frac{7300000}{3}\approx2433333.33\space m^{3}\)
This value is closest to \(2433400\space m^{3}\) (the slight difference is due to rounding during calculation).

Answer:

B. \(2433400\space m^{3}\)