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Circles

The Hook

The infinite loop.

What is it?

The set of all points equidistant from a center point.

Time Travel (History)

The wheel is arguably the most important invention in human history, entirely based on the circle.

Cheat Code

Cherry Pie is Delicious (C=πd). Apple Pies are too (A=πr²).

Practice This Now!

The Field Guide

In Plain English: A circle is the perfect shape. Pi (3.14) is the magic code that unlocks it. If you know how wide it is, multiply by Pi to see how far it is to walk around it.

In The Real World: Tires. A bigger tire covers more distance per rotation because its Circumference is larger.

How To Do It

  1. Find the Radius (r). If given Diameter, divide by 2.
  2. For Area: Square r, then multiply by 3.14.
  3. For Circumference: Multiply Diameter by 3.14.

Booby Trap!

Mixing up Radius (halfway) and Diameter (all the way). Formulas usually ask for r, but problems give you d.

Real World Challenge
"A pizza has a diameter of 20cm. How much cheese covers it (Area)?"
The Logic: Diameter 20 means Radius 10. A = πr². 10² = 100. 100 * 3.14 = 314 sq cm.

Training Drills

Formulas
A = πr² C = 2πr
Area is squared.