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To solve this problem, we need to determine the length of an 18-inch diameter pipe required to hold 900 imperial gallons.

### Step 1: Volume of a Cylinder Formula
The pipe is cylindrical, and its volume \( V \) can be calculated by the formula for the volume of a cylinder:
\[
V = \pi r^2 h
\]
Where:
- \( r \) is the radius of the cylinder (half the diameter),
- \( h \) is the height (or length in this case),
- \( \pi \) is approximately 3.1416.

### Step 2: Converting Units
- The diameter of the pipe is 18 inches, so the radius \( r \) is \( 9 \) inches.
- Convert the radius to feet because the answer choices are in feet. Since there are 12 inches in a foot:
\[
r = \frac{9}{12} = 0.75 \, \text{feet}
\]

- 1 imperial gallon is equivalent to 0.160544 cubic feet.

Thus, the total volume of 900 imperial gallons is:
\[
900 \, \text{gallons} \times 0.160544 \, \frac{\text{ft}^3}{\text{gallon}} = 144.4896 \, \text{cubic feet}
\]

### Step 3: Solve for the Length \( h \)
We now have:
\[
144.4896 = \pi (0.75)^2 h
\]
Solving for \( h \):
\[
h = \frac{144.4896}{\pi (0.75)^2}
\]
\[
h = \frac{144.4896}{\pi \times 0.5625}
\]
\[
h = \frac{144.4896}{1.767145867}
\]
\[
h \approx 81.7 \, \text{feet}
\]

### Conclusion:
The length of the pipe required is approximately **81.7 feet**, closest to answer choice **(c) 81.625 feet**.

Would you like further clarification or details on this solution? Here are 5 related questions for further practice:

1. How would the required pipe length change if the pipe diameter increased to 24 inches?
2. If the pipe was filled with water instead of an imperial liquid, would the volume calculation change?
3. What is the formula for calculating the surface area of the cylindrical pipe?
4. How do you convert imperial gallons to liters and then calculate the pipe length in a metric system?
5. What is the significance of using imperial gallons versus US gallons in calculations like this?

**Tip:** Always check your units to ensure they are consistent throughout your calculations.

An overflow tank is required to hold 900 imperial gallons. What length of 18" pipe would be required to meet this requirement?

Learn how to calculate the required length of an 18" diameter pipe to hold 900 imperial gallons of liquid using the volume of a cylinder formula. This problem involves geometry, unit conversion, and real-world application, suitable for Grades 10-12 students.

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