Answer
See below
Work Step by Step
(a)
:
First of all, convert all the dimensions that are the side of the square, base and height, into yards.
Since one yard is equal to\[3\text{ feet}\], one can convert the side of the square base as follows:
\[\begin{align}
& 756\text{ feet}=\frac{756\text{ ft}}{1}\times \frac{1\text{ yd}}{3\text{ ft}} \\
& =252\text{ yd}
\end{align}\]
Since one yard is equal to\[3\text{ feet}\], one can covert the height as follows:
\[\begin{align}
& 480\text{ feet}=\frac{480\text{ ft}}{1}\times \frac{1\text{ yd}}{3\text{ ft}} \\
& =160\text{ yd}
\end{align}\]
Now, in order to compute the volume of the pyramid, compute the area of the square base using the equation as shown below:
\[\begin{align}
& \text{Area of square base}\ \left( B \right)={{a}^{2}} \\
& ={{\left( 252\text{ yd} \right)}^{2}} \\
& =63,504\text{ y}{{\text{d}}^{\text{2}}}
\end{align}\]
Thus, the area of the square base is \[63,504\text{ fee}{{\text{t}}^{2}}\].
Now, compute the volume of the pyramid using the equation as shown below:
\[\begin{align}
& \text{Volume of the pyramid}=\frac{1}{3}Bh \\
& =\left( \frac{1}{3}\times 63,504\text{ y}{{\text{d}}^{2}}\times 160\text{ yd} \right) \\
& =3,386,880\text{ y}{{\text{d}}^{3}}
\end{align}\]
(b)
Now, in order to compute the number of stones required for the construction of the great pyramid, one is required to divide the volume of the pyramid with the average volume of the stone block.
Compute the number of stones required for constructing the pyramid using the equation as shown below:
\[\begin{align}
& \text{Required number of stone blocks}=\frac{\text{Volume of pyramid}}{\text{Volume of stone}} \\
& =\frac{3,386,880\text{ y}{{\text{d}}^{3}}}{1.5\text{ y}{{\text{d}}^{3}}} \\
& =2,257,920\text{ }
\end{align}\]
