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Circles

Overview

The infinite loop.

What is it?

The set of all points equidistant from a center point.

History

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

Key Idea

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

Practice This Topic

Concept Guide

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.

Real-world example: 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.

Common Pitfall

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

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

Practice Examples

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