AI Tutor
Ever wonder why a 16-inch pizza gives you nearly double the pizza of a 12-inch pie, even though it is only four inches wider?
The secret lies in how circle area grows, and understanding this unlocks everything from pizza sizes to dartboards and washer rings.

The Area of a Circle

The distance from the center of a circle to any point on its edge is the radius (rr), while the straight line passing all the way through the center is the diameter (dd), which is always twice the radius (d=2rd = 2r).
Around 250 BCE, the Greek mathematician Archimedes proved that slicing a circle into infinitely thin wedges rearranges it into a rectangle of length Ο€r\pi r and height rr, giving the formula for area: A=Ο€r2A = \pi r^2.
Let's find the area of a circular mirror with a diameter of 14Β cm14\text{ cm}.
First, cut the diameter in half to find the radius: r=14Γ·2=7Β cmr = 14 \div 2 = 7\text{ cm}. Now apply A=Ο€r2=π×72=49Ο€β‰ˆ153.94Β cm2A = \pi r^2 = \pi \times 7^2 = 49\pi \approx 153.94\text{ cm}^2.
A common trap is squaring the diameter instead of the radius, which makes your calculated area four times too big! Always halve the diameter before squaring.
What happens if you punch a smaller circular hole out of the middle of that circle, like a donut or a metal washer?

The Annulus

The ring-shaped region between two circles that share the same center point is called an annulus, coming from the Latin word for 'little ring'.
Circles that share the exact same center point are called concentric circles.