Answer
The quantity of the dirt to be removed to build the tunnel is\[3,768,000\text{ f}{{\text{t}}^{\text{3}}}\].
Work Step by Step
In order to determine the quantity of dirt to be removed to build the tunnel, one is required to compute the volume of the half cylindrical with dimensions as\[4\text{ meters}\], and\[50,000\text{ meters}\].
Compute the volume of the cylindrical tunnel using the equation as shown below:
\[\begin{align}
& \text{Volume of the semi cylindrical tunnel}=\frac{1}{2}\times \pi {{r}^{2}}h \\
& \text{=}\frac{1}{2}\times \left( \pi {{\left( 4\text{ ft} \right)}^{2}}\times 50,000\text{ ft} \right) \\
& =400,000\pi \text{ f}{{\text{t}}^{\text{3}}} \\
& =1,256,000\text{ f}{{\text{t}}^{\text{3}}}
\end{align}\]
Since, there are three semi cylindrical tunnels, compute the total quantity of dirt to be removed using the equation as shown below:
\[\begin{align}
& \text{Total quantity of dirt to be removed}=\text{Volume of one semi cylindrical tunnel}\times \text{3} \\
& =1,256,000\text{ f}{{\text{t}}^{3}}\times 3 \\
& =3,768,000\text{ f}{{\text{t}}^{\text{3}}}
\end{align}\]
