Cut, Rearrange, Almost a Rectangle
The same slices are shown twice — once cut from the circle, once laid out in a strip. Drag the slider to cut more, thinner slices and watch the strip's wavy edges flatten toward a plain rectangle, height r and width close to π·r.
6 sectors — width ÷ height = 3.46 (π ≈ 3.14)
Drag the slider right to cut the circle into more, thinner sectors.
- Sectors
- 6
- Strip height
- 0.87 r
- Strip width
- 3.02 r
- Target (a true rectangle)
- π r ≈ 3.14 r
Jump to a count
Ready to try some? Area of a circle worksheets
Where it usually goes wrong
πr² is handed over with the reason for the π left out — a rectangle's area is obviously length times width, but a circle has no length or width to multiply, so the formula lands as something to trust rather than something derived, and "why r squared" gets no answer better than "that's the formula."
Try this
- Press "4". The strip is four fat, wedge-shaped pieces with a noticeably bumpy top and bottom — nothing like a rectangle yet, and the width-to-height ratio in the readout is well short of π.
- Drag the slider from 4 up toward 32, watching the strip rather than the circle. The bumps on the top and bottom edges visibly shrink, and the readout's ratio creeps closer to 3.14.
- Press "32" and compare the strip's outline to the faint dashed rectangle behind it — height r, width πr. It is not exact, but the gap is now barely visible.
Where this goes next
The height of the strip is always the circle's own radius r, and its width is always half the circumference — so the strip's area, base × height, is (πr) × r = πr² however many sectors it was cut into; the formula is just that rectangle's area, arrived at sideways.