Why is the area of a circle πr²?
Why the area of a circle is πr²: cut the circle into slices, rearrange them into a near-rectangle of height r and width πr, and multiply.
Step-by-step explanation
- Imagine a circle of radius r, which we can cut into many equal pie slices.
- If we unroll and interlock these slices alternately, they form a shape resembling a rectangle.
- The height of this strip is the radius r, and its width is half the circumference, which is pi times r.
- Multiplying the width by the height gives us pi times r times r, which is pi r squared.
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