The Formulas Want the Radius

You'll learnto convert to the radius first, then feed it to area, circumference, arcs, and sectors.

Circle formulas run on the radius, arcs and sectors are a share of the whole, and the circle equation hides a sign trap. Watch where points quietly leak: the diameter used where the radius belongs, the arc or sector proportion set up against the wrong whole, and the center signs flipped or r² reported as r.

8 STEPS · 6 QUICK CHECKS · convert to radius first · center signs flip · v2

r, arcs, sectors

Before you start

What you're looking at

A single circle with its radius labeled r, the formulas area = πr² and circ = 2πr above it, beside a plan card.

The question

Is the given length a radius or a diameter, and what whole does a share divide?

Watch for

Watch every formula run on r; a diameter must be halved before it is used.

What the symbols mean

r is the radius; area = πr² and circ = 2πr are the formulas; the card lists three moves.

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