Water · Worked step by step
How many gallons are in 800 feet of 12 inch main?
If math has never been your thing, you are in the right place. Try it on paper first, then we write it out with you, one small step at a time, and explain every step in plain words so you never lose the thread.
The problem
A water main is 12 inches across and 800 feet long. How many gallons does it hold when full?
Grab a pen and paper first
Give it a real try on paper before you watch. If you get stuck, take a hint. If you go blank, that is fine, press play and we will walk it through together.
Watch it solved, with you
Every step is written out slowly and explained in plain words, so you always know what just happened. Nobody skips ahead and leaves you behind.
Press play and I’ll write it out with you, one small step at a time.
Every step gets a plain-words explanation here, so you always know exactly what just happened and why.
The written version, step by step
- 1
Change inches to feet
across = 12 in = 1 ft
- 12 inches divided by 12 is 1 foot.
- So the main is 1 foot across.
- That makes the circle simple.
- 2
Find the circle end
area = 0.785 × 1 × 1 • area = 0.785 sq ft
- Circle end is 0.785 times across times across.
- 1 times 1 is 1.
- So the area is just 0.785 square feet.
Quick trick: Anything times 1 stays the same, so a 1-foot pipe end is exactly 0.785.
- 3
Times length, then gallons
cubic feet = 0.785 × 800 = 628 • gallons = 628 × 7.48 = 4,697
- Multiply by the 800 foot length: 628 cubic feet.
- Then times 7.48 for gallons.
- That is about 4,697 gallons.
Quick trick: Estimate: 628 × 7.5 is about 4,710. The real answer is right there.
Remember this for good
A 12 inch main is exactly 1 foot across, which makes the circle simple: 0.785 times 1 times 1 is just 0.785.
12 inches is 1 foot, so the circle end is just 0.785 square feet. Then it is length times 7.48 like any pipe.
Solve it fast next time
- 12 inches is 1 foot, so the circle end is 0.785 square feet.
- Pipe gallons = circle times length times 7.48.
- A 1-foot pipe is the easiest case; the circle is just 0.785.
The answer: About 4,697 gallons.