The approximate volume of a cylindrical water tower is 7,540 ft3. The diameter of the water tower is 20 ft. What is the approximate height of the water tower?

1. Break Down the Problem

To find the height of the cylindrical water tower, we will need to use the formula for the volume of a cylinder:

$V = \pi r^2 h$

Where:

• $V$ = Volume
• $r$ = Radius
• $h$ = Height

Given:

• Volume, $V = 7,540 \, \text{ft}^3$
• Diameter, $d = 20 \, \text{ft}$

Since the radius $r$ is half of the diameter, we can calculate:

$r = \frac{d}{2} = \frac{20}{2} = 10 \, \text{ft}$

2. Relevant Concepts

Using the volume formula for the cylinder, we will rearrange the formula to solve for the height $h$:

$h = \frac{V}{\pi r^2}$

3. Analysis and Detail

Now, we will substitute the known values into the equation:

1. First, calculate $r^2$:

$r^2 = (10 \, \text{ft})^2 = 100 \, \text{ft}^2$

2. Substitute $V$ and $r^2$ into the height formula:

$h = \frac{7540 \, \text{ft}^3}{\pi \times 100 \, \text{ft}^2}$

3. Calculate $\pi \times 100$:

$\pi \approx 3.14 \Rightarrow \pi \times 100 \approx 314 \, \text{ft}^2$

4. Now divide:

$h = \frac{7540 \, \text{ft}^3}{314 \, \text{ft}^2} \approx 24.0 \, \text{ft}$

4. Verify and Summarize

We have substituted and calculated all appropriate values. The height of the water tower is approximately 24.0 feet.

Final Answer

The approximate height of the water tower is $24.0 \, \text{ft}$.