Area of a Circle
Every circle in the universe hides the same number. Cut one into slices and it rearranges into a shape you already know.
Cut it openArea of a Circle — explained
Slice a circle finely and lay the slices head-to-tail: they form a rectangle. Its height is the radius r; its length is half the way around, πr. Area = πr × r = πr². The formula is built, not handed over.
Worked example — Area of a Circle
Use it once, fully
A circular table has radius 3 m. What is its area?
- Write the relationship: A = πr²
Start from the built formula, not a remembered string.
- Substitute r = 3 → A = π × 3²
Square the RADIUS first — the square belongs to r alone, not to πr.
- 3² = 9, so A = 9π ≈ 28.3 m²
Leaving 9π exact is honest; the decimal is only for the real table.
AnswerA = 9π ≈ 28.3 m²
The idea — Area of a Circle
A = πr² — and it runs backwards just as well: r = √(A ÷ π).
A formula you can rearrange is a formula you own.
Questions about Area of a Circle
What is the formula for the area of a circle?
The area of a circle is A = πr², where r is the radius. It comes from slicing the circle into thin pieces and rearranging them into a rectangle with height r and length πr.
How do you find the area of a circle with radius 3 meters?
Substitute r = 3 into A = πr² to get A = π × 9 = 9π, which is approximately 28.3 square meters.
Why do you square only the radius and not πr?
In A = πr², the square applies to r alone because the formula is built from a rectangle whose sides are r and πr multiplied together, not (πr) squared.
Can you find the radius if you know the area?
Yes, the formula rearranges to r = √(A ÷ π), letting you work backwards from area to radius.
You've seen the idea. Now make it stick.
The journey continues in Zeeza — free to start, made to adapt to how you learn.
- Explain it in your own words — and master it
- …and more, adapted to you