Answer
The cost of filling the pool is\[\$27\].
Work Step by Step
First of all, compute the radius of the pool using the equation as shown below:
\[\begin{align}
& \text{Radius}=\frac{1}{2}\times \text{Diameter} \\
& =\frac{1}{2}\times 24\text{ feet} \\
& =12\text{ feet}
\end{align}\]
In this way,
\[r=12\text{ feet}\], and \[h=4\text{ feet}\]
In order to determine the cost of filling the pool, one is required to compute the volume of the circular shaped pool with dimensions as\[r=12\text{ feet}\], and\[h=4\text{ feet}\].
Compute the volume of the right circular cylinder using the equation as shown below:
\[\begin{align}
& \text{Volume of the right circular cylinder}=\pi {{r}^{2}}h \\
& \text{=}\left( \pi {{\left( 12\text{ ft} \right)}^{2}}4\text{ ft} \right) \\
& =\text{576}\pi \text{ f}{{\text{t}}^{\text{3}}} \\
& =1,810.28\text{ f}{{\text{t}}^{\text{3}}}
\end{align}\]
Thus, the quantity of water for filling the pool is\[1,810.28\text{ f}{{\text{t}}^{\text{3}}}\].
Now, compute the number of gallons of water required to fill the pool as follows:
\[\begin{align}
& \text{Number of gallons required to fill pool}=\text{Volume of the tank}\times \\
& \text{Capacity of one cubic feet} \\
& =1,810.28\text{ f}{{\text{t}}^{\text{3}}}\times 7.48 \\
& =13,541\text{ f}{{\text{t}}^{\text{3}}}
\end{align}\]
Now, compute the cost of filling the pool using the equation as shown below:
\[\begin{align}
& \text{Cost to fill the pool}=\text{Number of gallons required to fill the pool}\times \\
& \text{Cost of water per thousand gallons} \\
& =13,541\times \frac{\$2}{1000}\\&=\$27\end{align}\]
