Water and wastewater · Worked step by step
What is the area of a 20 foot round clarifier?
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 round clarifier is 20 feet across. What is its surface area?
Grab a pen and paper first
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Watch it solved, with you
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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
Write what you know
across = 20 ft
- The clarifier is a circle, 20 feet across.
- For a circle we use the 0.785 factor.
- That is all we need for the area.
- 2
Use the circle factor
area = 0.785 × 20 × 20 • area = 314 sq ft
- First 20 × 20 = 400.
- Then 400 × 0.785 = 314.
- So the area is 314 square feet.
Quick trick: 20 × 20 = 400 is easy; 400 × 0.785 is 314. Do the squaring first.
Remember this for good
The area of a circle is 0.785 times the width times the width. The answer is in square feet.
A circle is about 78.5% of the square around it, so 0.785 is the circle factor. Width times width times 0.785 gives the round area.
Solve it fast next time
- Round area = 0.785 times across times across.
- Across is the diameter, not the radius.
- Area is always in square feet, because you multiplied feet by feet.
The answer: 314 square feet.