Circles — Area, Circumference, Arcs, Sectors

ACT Math · Axiom Academy

LESSON Circles: Area, Circumference, Arcs & Sectors ACT Math — Plane Geometry. One idea unlocks every circle question: a part of a circle is just a fraction of the whole. Watch the radius sweep the whole disk — that swept region is the area , . Then the rim unrolls into a straight strip — its length is the circumference , . Two motions, two formulas. Area — the region swept by the radius Circumference — the rim, unrolled A circle has a diameter of 10. Find its area and circumference. 2. Arc Length — a Fraction of the Rim An arc is a portion of the circumference. As the central angle opens, the highlighted arc grows — and the fraction bar shows exactly what portion of the full rim it covers. The arc length is that fraction of . degrees — the fraction of the circumference radians — the same idea, angle measured differently Find the length of a arc on a circle with radius 10. 3. Sector Area — the Pizza Slice A sector is a "pizza slice" — the region between two radii and the arc. As sweeps open, the slice fills in. It is the same fraction of the whole area . degrees — the fraction of the area A pizza has a diameter of 16 inches. If a slice has a central angle of , what is the area of the slice? Worked Example — Working Backwards A sector of a circle with radius 6 has an area of . What is the central angle? 4. Central vs. Inscribed Angles

This is the written version of the interactive lesson above. See the full ACT Math course.