Question

quiz 3: volumes of solids
angel visited the great pyramid of giza in egypt and learned that the pyramid was originally 481 feet tall and its square base had sides measuring 751 feet in length. angel wants to know the volume of the pyramid. what is the volume of the pyramid?
\\(1.2 \times 10^5\\,\text{ft}^3\\)
\\(4.5 \times 10^7\\,\text{ft}^3\\)
\\(3.6 \times 10^5\\,\text{ft}^3\\)
\\(9.0 \times 10^7\\,\text{ft}^3\\)

Explanation:

Step1: Recall Pyramid Volume Formula

The volume \( V \) of a square - based pyramid 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 \( B = s^{2}\). So the formula for the volume of a square - based pyramid can also be written as \( V=\frac{1}{3}s^{2}h \).

Step2: Identify the values of \( s \) and \( h \)

We are given that the side length of the square base \( s = 751\) feet and the height of the pyramid \( h = 481\) feet.

Step3: Calculate the area of the base \( B \)

First, calculate the area of the square base. \( B=s^{2}=(751)^{2}\). Let's calculate \( 751\times751\):

$$
LATEXBLOCK0
$$

Step4: Calculate the volume \( V \)

Now, use the volume formula \( V=\frac{1}{3}Bh=\frac{1}{3}\times B\times h\). Substitute \( B = 564001\) and \( h = 481\) into the formula:
\( V=\frac{1}{3}\times564001\times481\)
First, calculate \( 564001\times481\):

$$
LATEXBLOCK1
$$

Then, divide by 3: \( V=\frac{271284481}{3}\approx90428160.33\approx9.0\times10^{7}\) (when we round to a reasonable number of significant figures. Let's check the approximation: \(\frac{271284481}{3}\approx90428160\), and \(90428160\approx9.0\times10^{7}\) since \(90428160 = 9.042816\times10^{7}\approx9.0\times10^{7}\) when considering significant figures or approximate value for the multiple - choice options)

Answer:

\(9.0\times10^{7}\text{ ft}^3\) (the option with \(9.0\times10^{7}\text{ ft}^3\))