Circles & Arc Measures
📋 What it is
A circle's circumference is π times its diameter; an arc is a slice of that edge measured in degrees.
🗣️ Coach says
Every circle hides the same magic number: circumference ÷ diameter is always π (~3.14), no matter the size. Arcs are just fractions of the trip around — a 90° arc is a quarter of the circumference.
🧠 Memory hook
C = π × d. The diameter goes ALL the way across; the radius is HALF (to the middle).
😂 Giggle
What did the circle say on its birthday?
"Time to get around to celebrating!"
😲 Whoa!
π has been calculated to over 100 trillion digits — but engineers rarely need more than about 15 to build anything, even a spacecraft.
✅ Quick check: A circle has diameter 10 cm. Roughly what is its circumference?
Say your answer out loud first — then reveal.
About 31.4 cm (π × 10).
Circumference = π × diameter, and π ≈ 3.14.
🧪 Try it! (2 minutes)
Wrap a string around a round lid, then across it. The way-around is always ~3× the way-across.